Chapter 6.4, Problem 4CCYP

To determine

To find:the trend in sales of fax machine suggested by the graph.

Answer to Problem 4CCYP

The graph suggest that after $1990$ the annual sales in million dollar will be maximum at $\text{1992}\text{.121year}$ and the maximum amount will be $\text{1339}\text{.628}$ millions dollar.

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:

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

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:

  

The graph suggest that after $1990$ the annual sales in million dollar will be maximum at $\text{1992}\text{.121year}$ and the maximum amount will be $\text{1339}\text{.628}$ millions dollar after that the sales will reduced which can be seen from the graph that the slope reduce which means sales will reduce.

Hence,The graph suggest that after $1990$ the annual sales in million dollar will be maximum at $\text{1992}\text{.121year}$ and the maximum amount will be $\text{1339}\text{.628}$ millions dollar.