Q. 19 - Calculus

Question

Considering the discussion at the end of the stoplight example in the reading, would you expect that the area under the graph of a function f is related to the derivative f'? Or would you expect that the area under the graph of a derivative function f' is related to the function f? 

Step-by-Step Solution

Answer

The area under the graph of the function f' is related to the function f.

Step 1. Given Information

The given statement is that the area under the graph of a function f is related to the derivative f'

Step 2. Explanation

Let v(t) represents velocity and s(t) represents distance.

In the example, $v\left(t\right)=s\text{'}\left(t\right)$

Thus, we can conclude that the area under the graph of the function f' is related to the function f.