For the function

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

For the function

f(x)=x^{2}+1

, answer the following: (i) Find the average rate of change of

f

from

x=1

x=3

. (ii) Find

f'(2)

. State which of the two results obtained in (i) and (ii) is greater.

Related theory

Differentiation Rules
Derivative Foundations
Differentiation from first principles
Intuitive idea of derivatives
Limits and Derivatives

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