Which of the following statements must be true if is differentiable at ?

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

Problem

Which of the following statements must be true if

f

is differentiable at

x=2

? (a)

f'

is continuous at

x=2

. (b)

f

is continuous at

x=2

. (c)

f

is differentiable on an open interval containing

x=2

. (d)

f

may be discontinuous at

x=2

provided

f'(2)

exists.