Chapter 2.3, Problem 35PPS

(a)

To determine

To find: Plot the graph of the function $f\left(x\right)=x^2$ .

Answer to Problem 35PPS

The graph of the function is shown below.

Explanation of Solution

Given information:

The equation of the graph is given as:

  $f\left(x\right)=x^2$

The graph of the function $f\left(x\right)=x^2$ is given as below:

$x$	$1$	$-1$
$f\left(x\right)$	$1$	$1$

  

Therefore, the graph of the function is shown above.

(b)

To determine

To find: Complete the given table of the function $f\left(x\right)=x^2$ .

Answer to Problem 35PPS

The table of the function is shown below.

Explanation of Solution

Given information:

The table of the function is given as:

  

To find the slope of the given function, first, calculate the derivative of the function and then substitute the given values of corresponding $x$ in the table above.

The value of the table of the function $f\left(x\right)=x^2$ is given as below:

$x$	$-4$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$
$f\left(x\right)$	$16$	$9$	$4$	$1$	$0$	$1$	$4$	$9$	$16$
slope		$-6$	$-4$	$-2$	$0$	$2$	$4$	$6$	$8$

Therefore, the table of the function is shown above.

(c)

To determine

To find: To observe what happens to the rate of change of the function as $x$ increases.

Answer to Problem 35PPS

The rate of change for $f\left(x\right)=x^2$ is increases as $x$ increases.

Explanation of Solution

As the graph shown above describes that, as $x$ increases so, $f^{\prime }\left(x\right)$ is increases, so,

The rate of change for $f\left(x\right)=x^2$ is increases as $x$ increases.

Therefore, the rate of change for $f\left(x\right)=x^2$ is increases as $x$ increases.