Chapter 2.2, Problem 83E

(a)

To determine

To apply: The leading coefficient test.

Explanation of Solution

Given information:

  $f(x)=x^3-25x$

Graph:

By leading coefficient test:

As the x³is a leading variable and its coefficient is 1 which is a positive coefficient.

And x is having odd number as its degree.

So when the large cubes were taken than x³ will be dominating

For $x<0$ negative large values, are taken and the answer will be a negative number so the graph falls for $x<0$ .

For $x>0$ positive large values, are taken and the answer will be a positive number so the graph increases for $x>0$ .

The graph will be:

  

(b)

To determine

To find: The real zeroes of the polynomial.

Explanation of Solution

Given information:

  $f(x)=x^3-25x$

Graph:

The roots of the equation $f(x)=x^3-25x$

  $\begin{array}{l}{x}^3-25x=0\\ x(x^2-25)=0\\ x(x+5)(x-5)=0\\ \text{zeros}=0,\text{ 5 , -5}\end{array}$

The curve will pass through -5, 0 and 5.

  

(c)

To determine

To draw: The sufficient solution points.

Explanation of Solution

Given information:

  $f(x)=x^3-25x$

Graph:

Plotting points:

  $f(x)=x^3-25x$

F(x)	x
24	-1
0	0
-24	1

So the curve also passes through (-1, 24), (0, 0), (1, -24)

  

(d)

To determine

To draw: A continuous curve for the points.

Explanation of Solution

Given information:

  $f(x)=x^3-25x$

Graph:

Continuous curve through the points

Points are:(-5,0) (-1,26) (0,0) (1,-24) (5,0)