(a) Define the derivative of a function at a point using first principles. (b)…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

(a) Define the derivative of a function

f(x)

at a point

x=a

using first principles. (b) Describe briefly what information the sign of

f'(a)

gives about the behaviour of the function near

x=a

. (c) Let

f(x)=\sin x

. Using your definition from part (a), state the value of

f'(0)

and interpret your answer with respect to the tangent at the origin.

Related theory

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

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