Chapter 2.2, Problem 44E

Solution

To draw the graph of the given polynomial.

  

Given:

  $f\left(x\right)=-x^4+8x$

Calculation:

Consider,

  $f\left(x\right)=-x^4+8x$

The degree is 4 and the leading coefficient is $-1$ .

Here the degree is odd and the leading coefficient is positive.

So, $f\left(x\right)\to -\infty$ as $x\to +\infty$ and $f\left(x\right)\to -\infty$ as $x\to -\infty$ .

When $x=-2$ ,

  $\begin{array}{c}f\left(-2\right)=-{\left(-2\right)}^4+8\left(-2\right)\\ =-32\end{array}$

When $x=-1$ ,

  $\begin{array}{c}f\left(-1\right)=-{\left(-1\right)}^4+8\left(-1\right)\\ =-9\end{array}$

When $x=0$ ,

  $\begin{array}{c}f\left(0\right)=-{\left(0\right)}^4+8\left(0\right)\\ =0\end{array}$

When $x=1$ ,

  $\begin{array}{c}f\left(1\right)=-{\left(1\right)}^4+8\left(1\right)\\ =7\end{array}$

When $x=2$ ,

  $\begin{array}{c}f\left(2\right)=-{\left(2\right)}^4+8\left(2\right)\\ =0\end{array}$

So the table of values is,

$x$	$-2$	$-1$	$0$	$1$	$2$
$y$	$-32$	$-9$	$0$	$7$	$0$

Now the graph is,