Suppose that f is a function given as f(x) = 4x – 3. We will compute the derivative of f at x = 2 as follows. Simplify the expression f(2 + h). f(2 + h) = f(2 + h) – f(2) Simplify the difference quotient, h f(2 + h) – f(2) h Rationalize the numerator of difference quotient. (If applies, simplify again.) f(2 + h) – f(2) The derivative of the function at x is the limit of the difference quotient as h approaches zero. f(2 + h) – f(2) f'(2) = lim h+0 h

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Suppose that f is a function given as f(x)
/4x – 3. We will compute the derivative of f at x = 2 as
follows.
Simplify the expression f(2 + h).
f(2 + h) =
f(2 + h) – f(2)
Simplify the difference quotient,
h
f(2 + h) – f(2)
h
Rationalize the numerator of difference quotient. (If applies, simplify again.)
f(2 + h) – f(2)
The derivative of the function at x is the limit of the difference quotient as h approaches zero.
f(2 + h) – f(2)
f'(2) = lim
h→0
Transcribed Image Text:Suppose that f is a function given as f(x) /4x – 3. We will compute the derivative of f at x = 2 as follows. Simplify the expression f(2 + h). f(2 + h) = f(2 + h) – f(2) Simplify the difference quotient, h f(2 + h) – f(2) h Rationalize the numerator of difference quotient. (If applies, simplify again.) f(2 + h) – f(2) The derivative of the function at x is the limit of the difference quotient as h approaches zero. f(2 + h) – f(2) f'(2) = lim h→0
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