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

6 0

3 years ago

The temperature in the Arctic Circle at 9:00am was 22.8° below zero. By 6:00pm on the same day, the temperature had decreased by

rosijanka [135]

4.65 is the new temperature.

8 0

3 years ago