Question

The function f(x)=4x+9x^-1 has one local minimum and one local maximum.

Question:
This function has a local minimum at x=______ with a value _______ and a local maximum at x=________ with value _______?

Answer 1

Take the derivative of the function f(x) and set it equal to zero. Solve for x

f'(x) = 4 - 9x^-2. = 0
4 = 9/x^2
x^2 = 9/4
x = +___ or - ___

That tells you where the maxima and minima are. The second derivative tells you which it is. It is a maximum where f'(x) = 0 and f''(x) is negative.

This is basic important stuff. You should be asking how to do them, not what the answers are. Otherwise you won't learn the subject.