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

The objective is to find one of the graph is shown as a function f and the other is its derivative

Now, to determine the graph of a function f from the graph of its derivative f'.

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

and (0.8,2.6), and increasing on the interval (-1,0.8) and (2.6,$\infty$).

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

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

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