Ap calculus: f" = 4x^3 - 2x, critical nums of f: -1, 0, 1

[joy08]

let f''=4x^3-2x and let f(x) have critical numbers -1,0, and 1. Use the second derivative test to determine if any of the critical numbers gives a relative maximum.

I did this:

for -1:

4(-1)^3 - 2(-1) = -2 maximum

for 0:

4(0)^3 - 2(0) = 0 inflection point

for 1:

4(1)^3 - 2(1) = 2 minimum

 

[o_O]

Re: Ap calculus

Correct except for x = 0. If you are given that it is a critical point and f"(x) = 0, it does not tell you anything as it could be a relative maximum/minimum or neither at that point. So, you must resort to some other method in determining its nature.