Suppose gives the temperature (in °C) of a liquid at time minutes

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

Problem

Suppose

g(t)

gives the temperature (in °C) of a liquid at time

t

minutes. A student considers two ways to approximate

g'(6)

: • Method A uses

g(6)

and

g(6.2)

. • Method B uses

g(5.8)

and

g(6.2)

. In one or two sentences, state which method is expected to yield the better estimate of

g'(6)

and briefly explain why.

Related theory

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

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