Chapter 4.8, Problem 50E

(a)

To determine

To find: the zeros, local maximum and local minimum values of the function.

Answer to Problem 50E

The zeros are $\left(-3,0\right)$ , local maximum is $\left(-2,4\right)$ and local minimum is $\left(0,0\right)$ .

Explanation of Solution

Given information:

The graph of a polynomial function is shown.

  

Calculation:

From the graph it is very clear that function crosses $x$ axis at $x=-3$ and touches at $x=0$ .

The graph has maximum value at point $\left(-2,4\right)$ and minimum at $\left(0,0\right)$ .

Therefore, the zeros are $\left(-3,0\right)$ , local maximum is $\left(-2,4\right)$ and local minimum is $\left(0,0\right)$ .

(b)

To determine

To compare: the $x$ intercepts of the graphs of $y=f\left(x\right)$ and $y=-f\left(x\right)$ .

Answer to Problem 50E

The $x$ intercept of graph $y=-f\left(x\right)$ and $y=f\left(x\right)$ is same.

Explanation of Solution

Given information:

The graph of a polynomial function is shown.

  

Calculation:

The graph of $y=-f\left(x\right)$ is reflection of graph of $y=f\left(x\right)$ over the $x$ axis.

The $x$ intercept of graph $y=-f\left(x\right)$ and $y=f\left(x\right)$ is same.

(c)

To determine

To compare: the maximum and minimum values of the functions $y=f\left(x\right)$ and $y=-f\left(x\right)$ .

Answer to Problem 50E

For the function $y=f\left(x\right)$ , local maximum is $\left(-2,4\right)$ and local minimum is $\left(0,0\right)$ .

For function $y=-f\left(x\right)$ , local maximum is $\left(-2,-4\right)$ and local minimum is $\left(0,0\right)$ .

Explanation of Solution

Given information:

The graph of a polynomial function is shown.

  

Calculation:

The graph of $y=-f\left(x\right)$ is reflection of graph of $y=f\left(x\right)$ over the $x$ axis.

For the function $y=f\left(x\right)$ , local maximum is $\left(-2,4\right)$ and local minimum is $\left(0,0\right)$ .

For function $y=-f\left(x\right)$ , local maximum is $\left(-2,-4\right)$ and local minimum is $\left(0,0\right)$ .