If a function is differentiable at

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

If a function

f(x)

is differentiable at

x=3

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

f'(x)

is continuous at

x=3

(b)

f(x)

is monotonic in some neighbourhood of

x=3

(c)

f(x)

is continuous at

x=3

(d)

\displaystyle \lim_{h\to0}\frac{f(3+h)-f(3)}{h}

is infinite