6. Consider the function f(x)= 2x3 - 6x2 – 18x+22. Use the Second Derivative Test to find the relative extrema, if any, of the function. (Give your answers as ordered pairs.) f' (2) = 6x2 - 12x -18 f'(x)=0
6. Consider the function f(x)= 2x3 - 6x2 – 18x+22. Use the Second Derivative Test to find the relative extrema, if any, of the function. (Give your answers as ordered pairs.) f' (2) = 6x2 - 12x -18 f'(x)=0
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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Transcribed Image Text:6. Consider the function f(x)= 2x° –6x² – 18x+22. Use the Second Derivative Test to find the relative
extrema, if any, of the function. (Give your answers as ordered pairs.)
f' (2) = 6x2 - 12x -18
f'(2): 0
( 3x +3)(2x-6) - o
3x +3 =0
dx -6-0
I= -1
3
fr (x) = 12x -12
f" (-) = -12- 12= -24
rmax
at x= - 24
1"(3)
36 - 12
24 sSo
rmin
at gH= 24
=
ニ
t(- 24) = 2(-24)3 -6( -24)2 -18(-24) + 22 = - 27338
f (24) = = 27094
2C 24)% - 6C 24)² - 18 (24)+ 22
(-24, -
Relative minimum(s): 24, 27094)
27338)
Relative maximum(s):
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