Q. 17 - Calculus

Question

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

Step-by-Step Solution

Answer

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

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