Chapter 6.4, Problem 4ACYP

To determine

To graph:the function by making the table.

Answer to Problem 4ACYP

The graph shows a parabola having maxima or turning point where the slope changes at $\left(2.121,1339.628\right)$ .

Explanation of Solution

Given:

  $\text{f}\left(\text{x}\right)\text{=-0}{\text{.17x}}^{\text{4}}\text{+6}{\text{.29x}}^{\text{3}}\text{-77}{\text{.65x}}^{\text{2}}\text{+251x+1100}$ .

Concept used:

The graph of the function $\text{f}$ is the set of all point in the plane of the form $\left(\text{x,f}\left(\text{x}\right)\right)$ .

The graph can be defined by the graph of $\text{f}$ and the equation for the graph will be $\text{y=f}\left(\text{x}\right)$ .

The tabular data of domain as $\text{x}$ and range $\text{y}$ while connecting the point to form curve which can be plot as graph using graphing calculator.

Calculation:

  $\text{f}\left(\text{x}\right)\text{=-0}{\text{.17x}}^{\text{4}}\text{+6}{\text{.29x}}^{\text{3}}\text{-77}{\text{.65x}}^{\text{2}}\text{+251x+1100}$ .

Table:

$\text{x}$	$\text{-2}$	$\text{-1}$	$\text{0}$	$\text{1}$	$\text{2}$
$\text{y}$	$\text{861}$	$\text{764}\text{.89}$	$\text{1100}$	$\text{1279}\text{.47}$	$\text{-1865}$

Here by collecting all domain $\text{x}$ and range $\text{y}$ graph of the function can be drawn.

The graph of given function $\text{f}\left(\text{x}\right)\text{=-0}{\text{.17x}}^{\text{4}}\text{+6}{\text{.29x}}^{\text{3}}\text{-77}{\text{.65x}}^{\text{2}}\text{+251x+1100}$ is:

  

Hereturning point here is $\left(2.121,1339.628\right)$ and the curve is open down ward since the sign of the highest degree coefficient is negative and highest degree itself is even so, the end behavior is down and down.

Hence, graph shows a parabola having maxima or turning point where the slope changes at $\left(2.121,1339.628\right)$ .