I'm supposed to find all critical numbers of the given function.(adsbygoogle = window.adsbygoogle || []).push({});

Book defines critical number c as the place where f'(c)=0 or where f is not differentiable.

1. g(x)= x + 1/x

2. f(x)= x ln (x)

work:

1. [tex] g'(x) = \frac{x^2 - 1}{x^2} [/tex]

c= 1, -1, 0

Zero is wrong however. I put it in the answer because the function is not differentiable at that point. So I'm guessing I have the definition of differntiable at a point wrong. The limit doesn't exist as x approaches 0 so I thought the function wouldnt be differentiable there.

2. f'(x) = lnx + x/x

c= 1/e and all numbers less than or equal to zero.

The book only lists 1/e so same problem here.

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# Homework Help: Critical values

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