Yes I am expected to estimate the max and min values. If i’m quite honest, I didn’t do so well with this unit so that’s why I had a lot of trouble with graphing polynomial functions.

No worries, chibi. That's why we're here to help each other.

The fact that your teacher wants you to estimate this point is a good sign, because then you know you haven't missed anything important.

Let's take a random polynomial in factored form:

f(x) = (x + 1)(x - 2)2(x + 3)3

You need to be mindful that if the multiplicity of a factor is 1, such as (x + 1), it's go directly through the x-axis like a linear equation.

If the multiplicity of a factor is 2, such as (x - 2)2, then it'll behave like a parabola. In fact, an exponent that is even, whether it be 2, 4, 6, etc., will always behave this way and will NOT cross the x-axis. 

If the multiplicity of a factor is 3, such as (x + 3)3, then it'll behave like a cubic. All odd exponent other than 1 will do this.

Now, in terms of finding the local min/max, let's say one happens to exists between x = -1 and x = 2, you pick values that are -1 < x < 2, such as x = -0.5, 0, and 1 to see what happens to the original function. You'll be able to analyze their outputs, and estimate where the change occurs.

Wow! Thanks @bio_man, that made it so much easier now I have officially completed this question.

Sweet, I marked it solved 👍