EXAMPLE 4 Find the derivative of the function f(x)=x²-8x + 4 at the number a.SOLUTION From the definition we havef'(a) = lim f(a+h) = f(a)h→0h= limz limh→0h→0= lim==h→0limh→0h− 8(a + h) + 4] - [a² − 8a + 4]h-8a-8h + 4 - a² + 8a - 4h

Answered: Image /qna-images/answer/66f18533-e103-45cd-8c42-ea0798ba948f.jpg

XAMPLE 4 Find the derivative of the function f(x)=x²-8x + 4 at the number a. OLUTION From the definition we have f(a+h)-f(a) h (a) = lim h→0 = lim h-0. lim h→0. = lim || h→0. = lim h→0 + h − 8(a + h) + 4] - [a² − 8a + 4] - h 8a-8h + 4- a² + 8a - 4 h

XAMPLE 4 Find the derivative of the function f(x)=x²-8x + 4 at the number a. OLUTION From the definition we have f(a+h)-f(a) h (a) = lim h→0 = lim h-0. lim h→0. = lim || h→0. = lim h→0 + h − 8(a + h) + 4] - [a² − 8a + 4] - h 8a-8h + 4- a² + 8a - 4 h

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter1: Getting Started

Section: Chapter Questions

Problem 24PQ

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Question

EXAMPLE 4 Find the derivative of the function f(x)=x²-8x + 4 at the number a.
SOLUTION From the definition we have
f'(a) = lim f(a+h) = f(a)
h→0
h
= lim
z lim
h→0
h→0
= lim
=
=
h→0
lim
h→0
h
− 8(a + h) + 4] - [a² − 8a + 4]
h
-8a-8h + 4 - a² + 8a - 4
h

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