Assume that f(x) is continuous in some open interval J that contains the
point a,
and limit of f’(x) as x(a exists. Prove that f is differentiable at
a and
f’(a)=limit of f’(x) as x(a
Mathematics Homework Solutions
#85851
Continuity Proof
Assume that f(x) is continuous in some open interval J that contains the point a, f'(x) exists for each x and limit of f'(x) as xa exists. Prove that f is differentiable at a and
f'(a)=limit of f'(x) as xa
keywords: differentiability
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