Question

Determine the graph of a function f from the graph of its derivative f'.

Short answer

The function f is shown in Graph II and its derivative f' is shown in Graph I.

Step-by-step solution

Step 1. Given 

The given two graphs are

Step 2. Explanation

Observed form the second figure, the function f must be decreasing on the interval (- ∞, - 1) and (1,3), and increasing on the interval (-1,1) and (3, ∞) .

So, the one of the possible sketch of a function f that has these characteristics is shown in the graph 11.

Therefore, the graph I indicates the derivative of a function f

Hence, the function f is shown in Graph II and its derivative f' shown in Graph I.

As we can find the local extremum using first derivative. From the above graph I, the function is decreasing at (-2,0) and (2,4) where f' <0 and increasing on (0,2). Therefore, the graph Il indicates the derivative of a function f.