) For which values of x is f '(x) zero? (Enter your answers as a comma-separated list.) x = (No Response) For which values of x is f '(x) positive? (Enter your answer using interval notation.) (No Response) For which values of x is f '(x) negative? (Enter your answer using interval notation.) (No Response) What do these values mean? f is (No Response) when f ' > 0 and f is (No Response) when f ' < 0. (b) For which values of x is f ''(x) zero? (Enter your answers as a comma-separated list.)

When the derivative of a function is equal to zero, then it occurs when we have either a local minimum or a local maximum point. So for our x-coordinates we can say

[tex]f'(x)=0\: at \:x=2, and\: x=-2[/tex]

2. For which values of x is f '(x) positive?

Whenever we have

[tex]f'(x)>0[/tex]

then function is increasing. Since if we could start tracing tangent lines over that graph, those tangent lines would point up.

[tex]f'(x)>0 \:at [-4,-2) \:and\:(2, \infty)[/tex]

3. For which values of x is f '(x) negative?

On the other hand, every time the function is decreasing its derivative would be negative. The opposite case of the previous explanation. So

[tex]f'(x) <0 \: at\: [-2,2][/tex]

4.What do these values mean?

[tex]f(x) \:is \:increasing\:when\:f'(x) >0\\\\f(x)\:is\:decreasing\:when f'(x)<0[/tex]

5.(b) For which values of x is f ''(x) zero?

In its inflection points, i.e. when the concavity of the curve changes. Since the function was not provided. There's no way to be precise, but roughly

at x=-4 and x=4