EXAMPLE 4 Video Example Find the derivative of the function f(x)=x²-9x + 8 at the numbers (a) 5 and (b) a. SOLUTION (a) From this definition we have the following. f(5+h)-f(5) f'(5) = lim h (b) = lim = lim h-o = lim h-D = lim = lim h-o = lim h-0 = lim 25+ h h - f(a) - 9(5 + h) +8 1)+8] - [(5)² - 9(5) +8] h 459h + 8 + 12 a + h) + 8] − [a² - h -[a²9a +8] -9a-9h+8-a² +9a-8 h As a check on our work in part (a), notice that if we let a = 5, then f'(a) = f'(5) =

Calculus: Early Transcendentals
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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
Video Example
Find the derivative of the function f(x) = x² - 9x + 8 at the numbers (a) 5 and (b) a.
SOLUTION
(a) From this definition we have the following.
f'(5)
f(5+h)-f(5)
h
(b)
= lim
= lim
h→0
= lim
h→0
f'(a):
h→0
= lim
= lim
=
h-o
h→0
= lim
h-0,
= lim
h→0
25+
Ra
h
h
- f(a)
) — 9(5 + h) + 8] - [(5)² − 9(5) + 8]
h
459h + 8 + 12
(a + h) + 8] − [a² -
h
- [a²-9a +8]
-9a-9h+ 8-a²9a-8
h
As a check on our work in part (a), notice that if we let a = 5, then f'(a) = f'(5) =
Transcribed Image Text:EXAMPLE 4 Video Example Find the derivative of the function f(x) = x² - 9x + 8 at the numbers (a) 5 and (b) a. SOLUTION (a) From this definition we have the following. f'(5) f(5+h)-f(5) h (b) = lim = lim h→0 = lim h→0 f'(a): h→0 = lim = lim = h-o h→0 = lim h-0, = lim h→0 25+ Ra h h - f(a) ) — 9(5 + h) + 8] - [(5)² − 9(5) + 8] h 459h + 8 + 12 (a + h) + 8] − [a² - h - [a²-9a +8] -9a-9h+ 8-a²9a-8 h As a check on our work in part (a), notice that if we let a = 5, then f'(a) = f'(5) =
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