Q 95. - Precalculus Enhanced with Graphing Utilities

Question

A function $f$ has a positive average rate of change on the interval $[2,5]$. Is $f$ increasing on $[2,5]$? Explain.

Step-by-Step Solution

Answer

A function $f$ has a positive average rate of change on the interval means $f\left(2\right)<f\left(5\right)$.  It is not neceassrily that $f$ is increasing on the interval $[2,5]$.

Step 1. Given information

A function $f$ has a positive average rate of change on $[2,5]$.

Step 2. Determine whether the function f is increasing on [ 2 , 5 ] ?

It is given that $f$ is positive on the interval, which means that starting point is less than the ending point on the $y$-coordinate, that is, $f\left(2\right)<f\left(5\right)$.

Therefore, conclude that the function can be increasing on some interval $[2,5]$ and decreasing on some other interval $[2,5]$.

Hence, it is not neceassrily that $f$ is increasing on the interval $[2,5]$.