Q. 3 - Calculus

Question

State the definition of what it means for a function $f$ to be increasing on an interval $I$and what it means for a function $f$ to be decreasing on an interval $I$.

Step-by-Step Solution

Answer

If for all $a$ and $b$ in the interval $I$ with $b>a$,$f\left(b\right)>f\left(a\right)$ then the function $f$ is increasing in the interval $I$.

If for all $a$ and $b$ in the interval $I$ with $b>a$, $f\left(b\right)<f\left(a\right)$ then the function $f$ is decreasing in the interval $I$.

Step 1. Given Information.

Given the function $f$ defined in the interval $I$.

Step 2. Increasing or Decreasing Function.

Determine where the function $f$ is increasing.

If for all $a$and$b$ in the interval $I$ with $b>a$,$f\left(b\right)>f\left(a\right)$ then the function $f$is increasing in the interval $I$.

Determine where the function $f$ is decreasing.

If for all  $a$and $b$ in the interval $I$ with $b>a$,$f\left(b\right)<f\left(a\right)$  then the function$f$ is decreasing in the interval $I$.