## Find all values for x where function is differentiable

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### Find all values for x where function is differentiable

I am given the function ƒ(x) = ((3x-6)^⅓) + 5

How do I find all of the values of x where the function is differentiable?
~ Jared Beach ~

jaredbeach
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### Re: Find all values for x where function is differentiable

You could start by taking the derivative, and see where that is undefined.

The Chaz
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### 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:

$3x-6=0$

$x=2$
Living in the pools, They soon forget about the sea...— Rush, "Natural Science" (1980)

MarkFL
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### Re: Find all values for x where function is differentiable

Makes perfect sense. Thank you.
~ Jared Beach ~

jaredbeach
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