The graph of y = f ′(x), the derivative of f(x), is shown below. given f(–4) = 2, evaluate f(4).

When constructing the graph of the function from the graph of the derivative, there are 2 important point to mention:

1) If the graph of the derivative has got x-intercepts, then they are the maximum and minimum points of the original function. When the derivative changes from increasing interval to decreasing one, then this point is maximum. And this point is minimum when the derivative changes from decreasing to increasing interval.

2) If the graph of the derivative is below the OX axis, then it corresponds to the decreasing interval of the real function and if the part of the graph is above the OX axis it is an increasing interval of the real function.

Applying these concepts into our problem, we find that (0,0) is a minimum point in our original function. Because derivative changes from decreasing to increasing in this point. Our original function will decrease until this point from point (-4,2) and it will increase from the minimum point till the point (4,2). f(4) = 2 in the original function and our original function looks like an absolute value function.

answer: finding the extract measurements and knowing the points

step-by-step explanation:

b

step-by-step explanation: