Question

) 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.)

Answer 1

Answer:

Check below, please

Step-by-step explanation:

Step-by-step explanation:

1.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

 $f'(x)=0\: at \:x=2, and\: x=-2$

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

Whenever we have  

 $f'(x)>0$

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

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

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

 $f'(x)$

4.What do these values mean?

 $f(x) \:is \:increasing\:when\:f'(x) >0\\\\f(x)\:is\:decreasing\:when f'(x)$

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