Answer to Question #15614 in Calculus for hsd
Determine all x (is a real number) at which f(x) = |x - 2| is differentiable and compute f'(x) if possible.
f(x) = |x - 2|
is defined by
f(x) = 2-x, for
f(x) = x-2, for x>=2
f'(x)=(2-x)' = -1,
f'(x)=(x-2)' = +1, for x>=2
Hence f is differentiable
at all points x<>2.
For x=2 the function is not
since the limits of f' to x from the left and from the right
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