If and for all

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

Problem

If

f'(1)=1

and

\frac{d}{dx}\bigl(f(2x)\bigr)=f'(x)

for all

x>0

, and if

f'(x)

is differentiable, then there exists a number

c\in(2,4)

such that

f''(c)

is equal to (1)

-\frac{1}{4}

(2)

-\frac{1}{8}

(3)

\frac{1}{4}

(4)

\frac{1}{8}

Related theory

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