Chapter 2.2, Problem 12Q

To determine

The $x-\text{intercept}$ of the graph of the function and decide where the function is increasing and decreasing.

Answer to Problem 12Q

  $x=0$ & $x=6$ are the required $x-\text{intercept}$ of the function $f\left(x\right)=0.4x\left(x-6\right)$ and the function is increasing in $\left[3,\infty \right)$ and decreasing in $\left(-\infty ,3\right]$ .

Explanation of Solution

Given information : Given function is $f\left(x\right)=0.4x\left(x-6\right)$ .

To find the $x-\text{intercept}$ of the function $f\left(x\right)=0.4x\left(x-6\right)$ , we need to solve the equation $g\left(x\right)=0$ .

Therefore,

  $\begin{array}{c}0.4x\left(x-6\right)=0\\ x\left(x-6\right)=0\\ x=0,6\end{array}$ .

Thus, $x=0$ & $x=6$ are the required $x-\text{intercept}$ of the function $f\left(x\right)=0.4x\left(x-6\right)$ .

To decide where the function is increasing and decreasing, we need to plot the graph of $f\left(x\right)=0.4x\left(x-6\right)$ .

  

Clearly, from the above graph, the function is increasing in $\left[3,\infty \right)$ and decreasing in $\left(-\infty ,3\right]$ .