EXAMPLE 4 Find the derivative of the function f(x) = x² - 3x + 5 at the number a. SOLUTION From the definition we have lim f '(a) = h 0 = lim = h→0 = lim h→0 = lim h→0 lim = h→0 + f(a+h)-f(a) h - 3(a + h) + 5] - [a² - 3a + 5] h - 3a - 3h + 5-a²2 + 3a - 5 h h
EXAMPLE 4 Find the derivative of the function f(x) = x² - 3x + 5 at the number a. SOLUTION From the definition we have lim f '(a) = h 0 = lim = h→0 = lim h→0 = lim h→0 lim = h→0 + f(a+h)-f(a) h - 3(a + h) + 5] - [a² - 3a + 5] h - 3a - 3h + 5-a²2 + 3a - 5 h 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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![EXAMPLE 4 Find the derivative of the function f(x) = x² - 3x + 5 at the number a.
X
SOLUTION From the definition we have
f '(a) = lim
=
=
11
lim
h→0
lim
h→0
lim
h→0
lim
h→0
[
a²
f(a+h)-f(a)
- 3(a + h) + 5] - [a² - 3a + 5]
h
h
3a - 3h + 5 - a² + 3a - 5
h
h](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05136949-0414-47eb-a73e-74f55563dd77%2Fd3ce2d05-5359-45ca-be1b-15b7c620c0c4%2F00mpuyk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:EXAMPLE 4 Find the derivative of the function f(x) = x² - 3x + 5 at the number a.
X
SOLUTION From the definition we have
f '(a) = lim
=
=
11
lim
h→0
lim
h→0
lim
h→0
lim
h→0
[
a²
f(a+h)-f(a)
- 3(a + h) + 5] - [a² - 3a + 5]
h
h
3a - 3h + 5 - a² + 3a - 5
h
h
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