Chapter 11.1, Problem 39E

Solution

To draw: The graph of function whose domain is $\left[0,5\right]$ and derivative at $x=2$ is $3$ .

The graph of function whose domain is $\left[0,5\right]$ and derivative at $x=2$ is $3$ is shown in figure (1).

Given information:

The domain of the function is $\left[0,5\right]$ .

The derivative of the function at $x=2$ is $3$ .

Calculation:

Since the derivative of the function is constant.

So the possible function should be linear.

Suppose the function is

  $y-y_0=m\left(x-x_0\right)$

Substitute $3$ for $m$

  $y-y_0=3\left(x-x_0\right)$

Also the derivative of the function at $x=2$ is $3$ implies that the line passes through the point $\left(x_0,y_0\right)=\left(2,0\right)$

Substitute $2$ for $x_0$ and $0$ for $y_0$

  $\begin{array}{c}y-0=3\left(x-2\right)\\ y=3x-6\end{array}$

  

Figure (1)