Chapter 4.2, Problem 39E

(a)

To determine

To sketch: The graph of the differentiable function $y=f(x)$ with given properties.

Answer to Problem 39E

The graph is:

  

Explanation of Solution

Given information:

The differentiable equation is: $y=f(x)$

The local minimum at $(1,1)$ and local maximum at $(3,3)$

Graph:

The graph of the function that has a local minimum at $(1,1)$ and a local maximum at $(3,3)$ is:

  

The graph must show a hump at the specified places that points both up and down.

(b)

To determine

To sketch: The graph of the differentiable function $y=f(x)$ with given properties.

Answer to Problem 39E

The graph is:

  

Explanation of Solution

Given information:

The differentiable equation is: $y=f(x)$

The local minimum at $(1,1)$ and $(3,3)$

Graph:

The graph of the function that has a local minimum at $(1,1)$ and a local minimum at $(3,3)$ is:

  

There must be two downward-pointing humps on the graph. (There must be an intermediate local maximum).

(c)

To determine

To sketch: The graph of the differentiable function $y=f(x)$ with given properties.

Answer to Problem 39E

The graph is:

  

Explanation of Solution

Given information:

The differentiable equation is: $y=f(x)$

The local maximum at $(1,1)$ and $(3,3)$

Graph:

The graph of the function that has a local maximum at $(1,1)$ and a local maximum at $(3,3)$ is:

  

There must be two upward-pointing humps on the graph. (There must be an intermediate local minimum)