Chapter 11.3, Problem 78E

To determine

To graph:

The following functions and conditions:

  $f\text{'}\left(x\right)<0$ For $x<1$

  $f\text{'}\left(x\right)\ge 0$ For $x>1$

  $f\text{'}\left(1\right)=0$

Explanation of Solution

Given information:

  $f\text{'}\left(x\right)<0$ For $x<1$

  $f\text{'}\left(x\right)\ge 0$ For $x>1$

  $f\text{'}\left(1\right)=0$

Graph:

  

Graph of function:

Interpretation:

According to the above condition the sketch of the quadratic function in form of $y=a{\left(x-1\right)}^2+k$ .

Where, $a>0$ the sketch of the modulus functions in form of $y=\left|x-1\right|$ .the graph will vary as per the constant.

By using the Desmos graph calculator, the considered function is drawn as above which shows that the graph of function.