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 October 10th, 2011, 05:22 PM #1 Member   Joined: Aug 2011 From: Alabama Posts: 93 Thanks: 0 Find all values for x where function is differentiable I am given the function ƒ(x) = ((3x-6)^?) + 5 How do I find all of the values of x where the function is differentiable?
 October 10th, 2011, 05:24 PM #2 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: Find all values for x where function is differentiable You could start by taking the derivative, and see where that is undefined.
 October 10th, 2011, 05:30 PM #3 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 461 Math Focus: Calculus/ODEs Re: Find all values for x where function is differentiable We are given: $f(x)=$$3x-6$$^{\small{\frac{1}{3}}}+5$ thus: $f'(x)=$$3x-6$$^{-\small{\frac{2}{3}}}$ Thus, we find f(x) is not differentiable for: $3x-6=0$ $x=2$
 October 10th, 2011, 05:36 PM #4 Member   Joined: Aug 2011 From: Alabama Posts: 93 Thanks: 0 Re: Find all values for x where function is differentiable Makes perfect sense. Thank you.

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# find all values of f for which the function is differentiable

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