Chapter 2.2, Problem 10P

Solution

To find: The interval of horizontal and vertical axes that describe a good view of graph of the function $s\left(x\right)=-4.10x^3+67.4x^2-121x+1170$ .

The required interval is $-57\le x\le 95,-830\le y\le 3000$ .

Given information:

The given function is $s\left(x\right)=-4.10x^3+67.4x^2-121x+1170$ .

Concept used:

End behavior of a function is the behavior of the graph as $x$ approaches positive infinity or negative infinity .For the graph of the polynomial function, the end behavior is determined by degree and sign of the leading coefficient.

Calculations:

First plot the graph of the given function:

  

To get the best view of the graph adjust the horizontal scale so that the end behavior of the graph as $x\to +\infty$ is visible and adjust the vertical scale so that the end behavior of the graph as $x\to -\infty$ is visible. Here degree is odd and the leading coefficient is negative then $f\left(x\right)\to +\infty \text{as}x\to -\infty \text{,}f\left(x\right)\to -\infty \text{as}x\to +\infty \text{,}$

The best view of graph is given below.

  

From then the interval of the horizontal axis is $-57\le x\le 95,-830\le y\le 3000$ .

Thus the required interval is $-57\le x\le 95,-830\le y\le 3000$ .