Post #5

Alright I'm so lost, and we have a test tomorrow. I have been all over Vacherie and Laplace trying to learn this.

The thing that I actually understand are the rules for the First and Second Derivative Test. But the problem is carrying out the problem and sometimes I don't understand what it is even asking for.

Okay, I'm most comfortable with the second derivative test rules:
1. take the derivative
2. then take the second derivative
3. set = to 0 (this gives you possible points of inflection)
4. set up intervals
5. plug in (tells you concave up/down, and finds the point of inflection)

Example problem: x^3-6x^2+12x
1. 3x^2-12x+12
2. 6x-12
3. 6x-12=0 x=2--->possible pts. of inflection
4. (-infinity,2) u (2,infinity)
5. 6(0)-12= -ve 6(3)-12= +ve
concave down concave up
x=2 is the point of inflection

It confuses me that I understand the rules, but I can't do a single problem. Especially problems that are like the ones on 3.6 homework quiz. The major thing I can't even start are problems like: find the points of inflection of f(x)=cosx-sinx on [0, 2pi] or something like: find any critical numbers for the function f(theta)=sin(theta)-cos^2(theta) with 0 (like number 2 on 3.1 homework quiz) Can someone help me on this?