Chapter 3, Problem 8SGA

To determine

To find: whether the function is monotonic on an interval $I$ if and only if the function is increasing on $I$ or decreasing on $I$ .

Answer to Problem 8SGA

$f\left(x\right)=x^2$ it is decreasing for $x<0$ and increasing for $x>0$ and the function is monotonic.

Explanation of Solution

Given:

A function is said to be monotonic, symmetric on an interval $I$ if and only if the function is increasing on $I$ or decreasing on $I$ .

Concept used:

A function is said to be monotonic on an interval $I$ if and only if the function is increasing on $I$ or decreasing on $I$ .

Calculation:

Let’s consider a function is said to be monotonic, symmetric on an interval $I$ if and only if the function is increasing on $I$ or decreasing on $I$ .

Need to determine whether the function is monotonic or symmetric.

A function is said to eb monotonic on an interval $I$ if and only if the function is increasing on $I$ or decreasing on $I$ .

For example: the graph of $f\left(x\right)=x^2$ shows that the function is decreasing for $x<0$ and increasing for $x>0$ .

Graph of $f\left(x\right)=x^2$ :

Hence, the function is monotonic and $f\left(x\right)=x^2$ it is decreasing for $x<0$ and increasing for $x>0$