Which of the following best defines the average rate of change of a differentiable…

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

Problem

Which of the following best defines the average rate of change of a differentiable function

f

on the closed interval

[a,b]

? (a)

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

(b)

\displaystyle\frac{f(b)-f(a)}{b-a}

(c)

\displaystyle\frac{1}{b-a}\int_{a}^{b} f(x)\,dx

(d)

\displaystyle\frac{f(a)-f(b)}{b-a}