Let -2x² + 6x - 3 for x < 0, | 522 – 3 for x > 0. According to the alternate form of the definition of the derivative, to compute f'(0), we need to compute the left-hand limit lim x-0 which is and the right-hand limit lim x 0+ which is We conclude that f'(0) is f(x) =

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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Let
-2x² + 6x
for x < 0,
for x > 0.
5 2 – 3
According to the alternate form of the definition of the derivative, to compute f'(0), we need to compute the left-hand limit
lim
x →0-
which is
and the right-hand limit
lim
x →0+
which is
We conclude that f'(0) is
f(x)
=
-3
Transcribed Image Text:Let -2x² + 6x for x < 0, for x > 0. 5 2 – 3 According to the alternate form of the definition of the derivative, to compute f'(0), we need to compute the left-hand limit lim x →0- which is and the right-hand limit lim x →0+ which is We conclude that f'(0) is f(x) = -3
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