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Calculus Question

Well, I’m kind of stuck here and I know we have some bright math fellas here and I would appreciate the help. I’m looking at the second derivative test and relative max’s and minimums. I’ll give an example problem then show where I’m missing something.

f(x)=x^3-5x^2+7x

Ok, so I find F prime of that and get my critical numbers, which are x=7/3 and x=1

Then I find f double prime and get:
f(x)=6x-10

I plug in my critical #'s, x=1 ends up being less than zero so that’s my local max and x=7/3 when plugged in yields a number >0 so it’s a local minimum.

So I have max (3) and min (7/3)

Now the problem I am having is the book gives this as the answer:
max: (1,3)
min: (7/3, 49/27)

I can not, for the life of me, figure out where the 1 and the 49/27 are coming from and the book doesn’t tell me where either. I’m assuming it’s something very simple that they didn’t feel the need to explain, but if anyone can tell me where the fuck those 2 numbers are coming from I’d appreciate it.

Also, does anyone know of any good calculus help websites? Maybe one with online lectures? I’m in math 125 right now, which is just basic calculus. I’ve found a few useful youtube videos, but I’m hoping there is something better.

Thanks guys.

The point (x, f(x)) is in the graph of your function. The book answers are what you have already calculated: the local maximum is at x = 1, and f(1) = 3; the local minimum is at x = 7/3, and f(7/3) = 49/27.

[quote]waylanderxx wrote:

Also, does anyone know of any good calculus help websites? Maybe one with online lectures? I’m in math 125 right now, which is just basic calculus. I’ve found a few useful youtube videos, but I’m hoping there is something better.

Thanks guys.[/quote]

We had to do a project at the end of the year where we found good websites that went over each chapter. Here is the best website I found: http://tutorial.math.lamar.edu/

[quote]Rational Gaze wrote:
The point (x, f(x)) is in the graph of your function. The book answers are what you have already calculated: the local maximum is at x = 1, and f(1) = 3; the local minimum is at x = 7/3, and f(7/3) = 49/27.[/quote]

Agreeing with this. Got a test on this next week.

Awesome thanks guys. Yah, I have to teach myself how to do optimization problems and how to differentiate exponential functions tonight. My asshole of a teacher just writes the concepts on the board and doesn’t do example problems. Makes us teach ourselves. Really fucking annoying.

[quote]waylanderxx wrote:
Awesome thanks guys. Yah, I have to teach myself how to do optimization problems and how to differentiate exponential functions tonight. My asshole of a teacher just writes the concepts on the board and doesn’t do example problems. Makes us teach ourselves. Really fucking annoying.[/quote]

LOl man im in the same boat as you. I mean really my teacher goes throught 2.5 hours of just concept shit its like cool bro…

Youtube videos are a godsend Ive been watching videos from JMTPatrick he is the fucken man. Here is an example video http://www.youtube.com/watch?v=-vwcLvb9A0s .

Another guy on youtube that is really good is MathTV guy he was really helpful as well
Example video http://www.youtube.com/watch?v=Lb8QrUN6Nck

[quote]optheta wrote:
waylanderxx wrote:
Awesome thanks guys. Yah, I have to teach myself how to do optimization problems and how to differentiate exponential functions tonight. My asshole of a teacher just writes the concepts on the board and doesn’t do example problems. Makes us teach ourselves. Really fucking annoying.

LOl man im in the same boat as you. I mean really my teacher goes throught 2.5 hours of just concept shit its like cool bro…

Youtube videos are a godsend Ive been watching videos from JMTPatrick he is the fucken man. Here is an example video http://www.youtube.com/watch?v=-vwcLvb9A0s .

Another guy on youtube that is really good is MathTV guy he was really helpful as well
Example video http://www.youtube.com/watch?v=Lb8QrUN6Nck[/quote]

This is very helpful thanks.

[quote]waylanderxx wrote:
Awesome thanks guys. Yah, I have to teach myself how to do optimization problems and how to differentiate exponential functions tonight. My asshole of a teacher just writes the concepts on the board and doesn’t do example problems. Makes us teach ourselves. Really fucking annoying.[/quote]

Welcome to higher education. The majority of math professors are a fucking joke and grad school ain’t much better. I had two professors in undergrad who literally did nothing but transcribe the class notes onto the board. It is literally no exaggeration to say that a high school kid could have taught the classes just as well. By sophomore year I would just go to class to count in the attendance and sit and do my homework so at least I was doing something worthwhile with that hour.

It is pretty sad that I am in grad school for applied math and I learn more off Wikipedia/Planet Math than I do from the actual lectures.

P.S. Feel free to hit me up with a PM if you need some help another time; I am constantly frustrated by how shittily most schools teach calc, so I am always happy to help somebody out.

[quote]jtrinsey wrote:
waylanderxx wrote:
Awesome thanks guys. Yah, I have to teach myself how to do optimization problems and how to differentiate exponential functions tonight. My asshole of a teacher just writes the concepts on the board and doesn’t do example problems. Makes us teach ourselves. Really fucking annoying.

Welcome to higher education. The majority of math professors are a fucking joke and grad school ain’t much better. I had two professors in undergrad who literally did nothing but transcribe the class notes onto the board. It is literally no exaggeration to say that a high school kid could have taught the classes just as well. By sophomore year I would just go to class to count in the attendance and sit and do my homework so at least I was doing something worthwhile with that hour.

It is pretty sad that I am in grad school for applied math and I learn more off Wikipedia/Planet Math than I do from the actual lectures.

P.S. Feel free to hit me up with a PM if you need some help another time; I am constantly frustrated by how shittily most schools teach calc, so I am always happy to help somebody out.[/quote]

All too true unfortunately. I’m about to graduate with a B.S. in applied math and I’ve had one good professor in my four years at university. I pretty much taught myself from the textbook for most courses. Many of the professors just don’t seem to give a shit and only teach because they have to.

[quote]Rational Gaze wrote:
The point (x, f(x)) is in the graph of your function. The book answers are what you have already calculated: the local maximum is at x = 1, and f(1) = 3; the local minimum is at x = 7/3, and f(7/3) = 49/27.[/quote]

Excellent explanation to the answer.

[quote]waylanderxx wrote:
Awesome thanks guys. Yah, I have to teach myself how to do optimization problems and how to differentiate exponential functions tonight. My asshole of a teacher just writes the concepts on the board and doesn’t do example problems. Makes us teach ourselves. Really fucking annoying.[/quote]

If you want someone who gives úber understandable examples go here:

And then just finish the series.

Once you got it down, you’ll pretty much never forget.

Aaah, I remember this. It was fun to learn, too bad I’ll never have use of it. lol

[quote]rcsermas wrote:
jtrinsey wrote:
waylanderxx wrote:
Awesome thanks guys. Yah, I have to teach myself how to do optimization problems and how to differentiate exponential functions tonight. My asshole of a teacher just writes the concepts on the board and doesn’t do example problems. Makes us teach ourselves. Really fucking annoying.

Welcome to higher education. The majority of math professors are a fucking joke and grad school ain’t much better. I had two professors in undergrad who literally did nothing but transcribe the class notes onto the board. It is literally no exaggeration to say that a high school kid could have taught the classes just as well. By sophomore year I would just go to class to count in the attendance and sit and do my homework so at least I was doing something worthwhile with that hour.

It is pretty sad that I am in grad school for applied math and I learn more off Wikipedia/Planet Math than I do from the actual lectures.

P.S. Feel free to hit me up with a PM if you need some help another time; I am constantly frustrated by how shittily most schools teach calc, so I am always happy to help somebody out.

All too true unfortunately. I’m about to graduate with a B.S. in applied math and I’ve had one good professor in my four years at university. I pretty much taught myself from the textbook for most courses. Many of the professors just don’t seem to give a shit and only teach because they have to. [/quote]

I hate to agree with this because it seems to just become an excuse for many students, but unfortunately this is true, though it is not exclusive to math. (I also have a B.S. in math, btw).

I’m not going to name schools because I find it difficult to believe it is different at most other schools, but it was no different for me than what you two have described, except I can honestly say I had two math teachers that seemed to enjoy teaching. One was a local actuary and only teaching a couple classes part time as a side job, the other wasn’t tenured either and left the year after I left the class for another position. In other words, I wouldn’t have recommended a single tenured professor in the math department.

It was never that big of a deal to me as I learn much better on my own as long as I have decent text. I’m just not an aural learner and had trouble paying attention in a classroom.

The solutions to these problems run much deeper than just getting some new teachers. The median quality of the student is also to blame and is declining at an extraordinary rate as the number of people to go to college increases. In a nutshell, I think universities have lost track of their original purpose and many departments are simply becoming research businesses that rely on the revenue stream created through mass education. Government (state and federal) only exasperates the problem with incentives to send more and more people to school. When college is available to all, regardless of actual intelect, you can only expect the quality to diminish and it is the above average students that end up being punished. We are seeing a similar effect in K-12 education. Instead of actually grouping students by intellect and providing them with different challenge relative to that intellect, we cater to the students of lowest and average intellect. Again, the best students are forced to suffer, and most don’t yet have the maturity or experience to realize the harm that is being done until it is too late. They are then perfectly willing to excel at mediocre tasks in the classroom, never to realize their full potential in the classroom.

[quote]tedro wrote:
It was never that big of a deal to me as I learn much better on my own as long as I have decent text. I’m just not an aural learner and had trouble paying attention in a classroom.

[/quote]

Same. For me, I have a hard time following someone else’s work as they present examples. I’m not sure why. Usually, I’ve read all the material and done all the homework for the lecture so I try to beat the instructor to the answer, on my own. But trying to follow along, I end up getting lost somewhere along the way, alot of times. Maybe because there’s alot of interruptions along the way so I start day-dreaming. I don’t know.

To tell the truth, I’d feel secure with just showing up for exams. However, in Calculus, the Prof. pretty much gives a graded quiz every class, so while attendance isn’t counted, you have to at least be there long enough to take the quiz.

Unlike you guys, I can’t learn squat on my own, attending classes and practices are a must.

Got my A in calculus, thank you very much, now onto functions of more variables.
http://www.fizika.unios.hr/cms/fizos/en/nastava/fizika/II_godina/3/m104.html

Well that test fucking sucked, looks like I’m going to be dropping it and retaking it next semester, awesome.

Gotta love calc. I’m in Math 150, which is our basic calc here. I got a 90 on the first exam and a 63 on the second, which i guess is ok because a 62 was the median score. Every friday we get 3 question quizzes so if you miss one part you automatically have a D.
I’m a computer engineering major, so i’m going to have to take Calc 1, Calc 2, Calc 3, Differential Equations, and Engineering Math…

[quote]Blaze_108 wrote:
Gotta love calc. I’m in Math 150, which is our basic calc here. I got a 90 on the first exam and a 63 on the second, which i guess is ok because a 62 was the median score. Every friday we get 3 question quizzes so if you miss one part you automatically have a D.
I’m a computer engineering major, so i’m going to have to take Calc 1, Calc 2, Calc 3, Differential Equations, and Engineering Math…[/quote]

Damn that is nuts. Yah, my average is like a 53 right now and the test I took just now raped me so…bye bye calc, cya in 2 months lol…FUCKKKK

Wow…I honestly have no idea how I passed that class.

Tedro,

You hit the nail on the head my man. I totally agree, the whole education system is catered toward the average, which is fine… but a lot of the kids who either have lower intellect or poor schooling when they are younger get washed out in the system and a lot of the smarter kids don’t get challenged and engaged enough.