Chapter 2.2, Problem 3P

Solution

To find: The interval for $x$ and $y$ that describe a good viewing window.

Given information:

  $f\left(x\right)=x^4-4x^2+2$

Calculation:

Using quadratic formula, the $x-$ intercept of the function,

  $\begin{array}{c}{x}^4-4x^2+2=0\\ x=-1.8,-0.8,0.8,1.8\end{array}$

Along $x-$ axis the viewing window is $\left[-4,4\right]$ .

Since the degree is even and leading coefficient is positive, the minimum value should be less than the lower value of $y-$ axis.

The maximum value of the function is 2. The upper $y$ value is more than 2.

So, the $y-$ axis viewing window is $\left[-4,4\right]$ .

Now, check the graph using viewing window.