Let , , and , each differentiable at . Which of the following correctly orders the…

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

Problem

Let

f(x)=x^2

g(x)=x^3

, and

h(x)=\sqrt{x}

, each differentiable at

x=1

. Which of the following correctly orders the instantaneous rates of change of the three functions at

x=1

from greatest to least? (a)

g'(1) > h'(1) > f'(1)

(b)

f'(1) > g'(1) > h'(1)

(c)

g'(1) > f'(1) > h'(1)

(d)

h'(1) > f'(1) > g'(1)