Consider the function

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

Problem

f(x)=x^{3}-5x+4

. For

c>1

, the average rate of change of

f

on the interval

[1,c]

equals the instantaneous rate of change of

f

x=2

. What is the value of

c

? (a)

2

(b)

\dfrac{-1+3\sqrt5}{2}

(c)

\dfrac{1+3\sqrt5}{2}

(d)

\dfrac{-1+\sqrt{45}}{3}