Chapter 3, Problem 62RE

To determine

To draw: The graph $f$.

Answer to Problem 62RE

Graph of $f$ from $f^{\prime }$.

  

Explanation of Solution

Given information:

  $f^{\prime }\left(x\right)=\{\begin{array}{l}-2,x<2\\ -0.5,x>2\end{array}$ , $f\left(0\right)=5$

From the given information we know the function $f\left(x\right)$ has the $y-$ intercept of $5$ . So the graph of $f\left(x\right)$ should be passing through the point $\left(0,5\right)$.

Let’s plot the point $\left(0,5\right)$.

The first derivative of $f\left(x\right)$ would give the slope of $f\left(x\right)$ . Hence draw a constant line through the point $\left(0,5\right)$ with the slope $-2$ . Then end the line on $x<2$.

Then change the direction of the line towards right on $x<2$ with a slope of $-5$.

Thus we can graph $f\left(x\right)$ of the given $f^{\prime }$.