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 _______?

asked by Daniela Davila
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.

posted by drwls

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