Question

u

Answer 1

In the interval -3 to approx -1.5 or -1.6, the function is decreasing and so f'(x) will be negative. It will be zero at approx -1.5 where it has a local minima.
Can you proceed in a similar fashion?

Answer 2

Are you given answer choices to pick from or are you supposed to provide a rough sketch?

Answer 3

No. f'(x) will be negative (below the x-axis) when f(x) is decreasing;
f'(x) will be above the x-axis when f(x) is increasing.
f'(x) will cross the x-axis exactly at those locations where f(x) has a local minima or maxima.

Answer 4

Are you given answer choices to pick from?

Answer 5

Are those the only two choices?

Answer 6

There are certain quick things to look for.
Look at the U-shaped part of f(x) to the right.
It is decreasing and then increasing.
In which answer choice does the corresponding f'(x) is negative for the decreasing part of the u-shape, crosses zero at the same point that the u-shape has a minimum and f'(x) becomes positive corresponding to theincreasing part of the u-shape?

Answer 7

The second option.

Answer 8

Notice how when f(x) is decreasing, the corresponding portion of f'(x) is negative (below the x-axis). When f(x) has a local minimum (or a maximum), f'(x) becomes zero (crosses the x-axis). When f(x) is increasing, the corresponding portion of f'(x) is positive (above the x-axis).

Answer 9

Yes. Red or brown it is hard to tell. But you posted just one link with two answer choices. It is the second one.

Answer 10

Yes.

Answer 11

Well, we have to choose from what is given. You said the other two choices are irrelevant and among the two choices the second one best fits f(x).

Even if you look at the left portion of f(x) and see where all it is increasing or decreasing and then look at the corresponding part of f'(x) you will see wherever f(x) is decreasing, f'(x) is negative and wherever f(x) is increasing, f'(x) is positive.