A post..Jan. 1, 2010!!

Ok, so to review a couple of things (at 3 o'clock in the morning..insomnia).

this is the second derivative test.

x^3 - 6x^2 + 12x

take the first derivative:

3x^2 -12x + 12

take the second derivative:

6x - 12

Set equal to 0 and solve:

x=2

Set up intervals:

(-inf., 2) U (2, inf.)

Plug in values within each interval:

-ve and +ve

And if the question asked you about the concavity, it would be concave up because you are going from decreasing to increasing.

So the above example problem is just basic, and I'm pretty sure if you were to get this problem on a test, you'd kill it. Now, maybe something a little more tedius? Perhaps?

Related Rates maybe...possibly?? Okay, so to start off on the steps:
1. Identify all of the variables and equations.
2. Identify what you want to find.
3. Sketch and label.
4. Write an equations involving your variables.
5. Take the derivative with in terms of time.
6. Substitute the derivative in and solve.

So say a spherical ball has a radius that in increasing at a rate of 4 cm/s. What is the change in volume when the radius equals 8 cm?

I get dr/dt = 4
r = 8

Since you are looking for dv/dt, you take the derivative of the volume formula. We know by definition that the volume of a spherical object is 4/3 pi r^3.

So:
dv/dt = 4/3 pi 3r^2 dr/dt

now plug in your respective data.
dv/dt = (4/3)(pi)3(8 cm)^2(4 cm/s)

Solve:
dv/dt = 1024pi cm^2/s.

And thats your answer!!! think you've got it! It really helps if you have a picture, but unfortunately I am at a loss to do so. See ya later!