Chapter 5.3, Problem 45E

To determine

To sketch : A smooth curve.

Explanation of Solution

Given information :

  $y=f\left(x\right)$ through the origin with properties that $f\text{'}\text{'}\left(x\right)<0$ for $x<0$ and $f\text{'}\text{'}\left(x\right)>0$ for $x>0$

Calculation :

Since, $f\text{'}\text{'}\left(x\right)<0$ for $x<0$ so the graph will have a negative slope for $x<0$ and $f\text{'}\text{'}\left(x\right)>0$ for $x>0$ so the graph will have a positive slope for $x>0$ .

The curve is drawn below:

Graph: