A differentiable function is defined on the closed interval and satisfies for every in .

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

A differentiable function

f

is defined on the closed interval

[2,6]

and satisfies

f'(x)\ge 3

for every

x

(2,6)

. (i) Explain why

f(2)<f(4)<f(6)

must hold. (ii) Show that

f(6)-f(2)\ge 12

, clearly indicating each logical step used.