Chapter 2.2, Problem 2P

Solution

To find intervals for $x$ and $y$ that describe a good viewing window for the graph of the polynomial function $f\left(x\right)=-x^3+36x^2-10$ .

The behaviour of the function is clearly visible when $x\in [-20,40]$ and $y\in [-4000,9000]$ .

Given:

  $f\left(x\right)=-x^3+36x^2-10$ .

Calculation:

Graph the function $f\left(x\right)=-x^3+36x^2-10$

with the help of a graphing calculator:

  

Adjust the dimensions of the window until the behaviour of the function is clearly visible:

  

Observe that the behaviour of the function is clearly visible when $x\in [-20,40]$ and $y\in [-4000,9000]$ .

Conclusion:

The behaviour of the function is clearly visible when $x\in [-20,40]$ and $y\in [-4000,9000]$ .