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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 _______?
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The derivative of the function f(x) needs to be equal to zero. There is a way to solve for x. f'(x) = 4 - 9x^-2. = 0 4 = 9/x^2 x^2 = 9/4 Either way, x is either + or - That tells you the location of the maxima and minima. The second derivative is the one that tells you which it is. It is a maximum where f'(x) = 0 and f''(x) is negative. This is the basics of important stuff. You should be asking how to do them, not what the answers are. You won't learn the subject if you don't learn the subject at all.
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