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Mathematics
Problem
Identify the condition that the two one-sided limits of the difference quotient
f
(
x
)
−
f
(
a
)
x
−
a
\dfrac{f(x)-f(a)}{x-a}
x
−
a
f
(
x
)
−
f
(
a
)
as
x
→
a
x\to a
x
→
a
must satisfy for
f
′
(
a
)
f'(a)
f
′
(
a
)
to exist.
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