Mathematics

Mathematics

Problem

For the function

f(x)=x^3-6x^2+9x+4

, let

A

denote the average rate of change of

f

on the interval

[1,3]

. Which of the following correctly compares

A

with the instantaneous rates of change

f'(1)

and

f'(3)

? a)

f'(1) < A < f'(3)

b)

A < f'(1) \text{ and } A < f'(3)

c)

A < f'(1) \text{ but } A > f'(3)

d)

A > f'(1) \text{ and } A > f'(3)

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