Chapter 4.1, Problem 33E

(a)

To determine

To describe: the $x$ values for which $f$ is increasing or decreasing.

Answer to Problem 33E

The function is increasing for $x>4$ and decreasing for $x<4$ .

Explanation of Solution

Given information:

Given graph is,

  

Calculation:

From the graph it is very clear that for all $x<4$ the $y$ value decreases as move from left to right and for all $x>4$ the $y$ value increases as move from left to right.

Therefore, the function is increasing for $x>4$ and decreasing for $x<4$ .

(b)

To determine

To describe: the $x$ values for which $f\left(x\right)>0$ .

Answer to Problem 33E

  $f\left(x\right)>0$ for $x<3\text{and}x>5$ .

Explanation of Solution

Given information:

Given graph is,

  

Calculation:

From the graph it is very clear that the graph is above $x$ axis for $x<3\text{and}x>5$ .

Therefore, $f\left(x\right)>0$ for $x<3\text{and}x>5$ .

(c)

To determine

To describe: the $x$ values for which $f\left(x\right)<0$ .

Answer to Problem 33E

  $f\left(x\right)<0$ for $3<x<5$ ..

Explanation of Solution

Given information:

Given graph is,

  

Calculation:

From the graph it is very clear that the graph is below $x$ axis for $3<x<5$ .

Therefore, $f\left(x\right)<0$ for $3<x<5$ .