Determine the critical numbers, if any, of the function 𝑓. 𝑓(𝑥)=3𝑥^4+3𝑥^3−54𝑥^2−81𝑥+21

Answer 1

Hey!

So first, in order to find the critical points of a function, we must take its derivative. This is a simple polynomial function, so using the power rule, we get:

12x³+9x² - 108 x-81

The last step is just setting this new function (f'(x)) equal to zero and finding the roots! Remember - before you try and factor it as a product of binomials, take out the GCF (greatest common factor). The degree of this function is 3, so you should end up with three roots at the end. (x=0 can be a critical point. )

Hope this helps!