Let on the interval .

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

Problem

Let

f(x)=x^{3}

on the interval

[1,2]

. (i) Show that there exists a number

\xi

(1,2)

such that

f'(\xi)

equals the average rate of change of

f

[1,2]

. (ii) Find one value of

\xi

that satisfies this condition.