Question

4: The function has a maximum of how many turns in its graph?

Answer 1

Given:

$f(x)=-x^4+4x^2-2$

To determine the maximum turns of the given function in its graph, we first note that the maximum number of turning points of a polynomial function is always one less than the degree of the function. Based on the given function, the degree is 4, so the turning points must be:

$Turning\text{ points = 4-1=3}$

We can double check this by graphing the function as shown below:

As we can see, there are 3 turns in its graph. Therefore, the answer is: D. 3