How can i describe the x-values at which f is differentiable at #f(x)=2/(x-3)# ? what is differentiable anyway ?

1 Answer
Jim H
Aug 21, 2017

Please see below.

Explanation:

Briefly, "differentiable" means "can be differentiated" and that mean "has a derivative".

The verb, "differentiate" means "find the derivative".
The noun "differentiation" is the act or process of differentiating, hence, the act or process of finding a derivative.

Definition

Function #f# is differentiable at #x=a# if and only if #f'(a)# exists.

For this function

#f(x) = 2/(x-3) = 2(x-3)^-1 = -1(x-3)^-2 = (-2)/(x-3)^2#

#f'(x)# sn defined for all #x# except #x=3#. So #f# is differentiable at every #x# except #x=3#.

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