For a function to be differentiable at

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

For a function

f

to be differentiable at

x=a

, which one of the following statements must be true? (a)

f

is continuous at

x=a

(b) Only the right-hand limit of

\dfrac{f(a+h)-f(a)}{h}

h\to0^{+}

exists (c) Both one-sided limits of

\dfrac{f(a+h)-f(a)}{h}

h\to0

exist and are equal (d) The sum of the two one-sided limits of

\dfrac{f(a+h)-f(a)}{h}

equals

0