3. A function and its first 2 derivatives are given. x² - 4x (x+4)² f(x) = = (x+4)³ (3x - 4) f'(x) f(x) ↑ or ↓? ƒ'(x) : = -24(x-4) (x + 4)4 f"(x) f(x) CU or CD? 4(3x-4) (x+4)3 a) Complete the table below using a + or - for the first derivative chart and use them to determine where f(x) is increasing/decreasing. ƒ"(x) = -24(x-4) (x+4)4 (-∞, -4) (-4, 4/3) + (-∞, -4) + b) Complete the table below using a + or - for the second derivative chart and use them to determine where f(x) is concave up/down. (-4,4) (4/3,00) (4,00) c) Determine the equations for Vertical/Horzontal Asymptotes co-ordinates of
3. A function and its first 2 derivatives are given. x² - 4x (x+4)² f(x) = = (x+4)³ (3x - 4) f'(x) f(x) ↑ or ↓? ƒ'(x) : = -24(x-4) (x + 4)4 f"(x) f(x) CU or CD? 4(3x-4) (x+4)3 a) Complete the table below using a + or - for the first derivative chart and use them to determine where f(x) is increasing/decreasing. ƒ"(x) = -24(x-4) (x+4)4 (-∞, -4) (-4, 4/3) + (-∞, -4) + b) Complete the table below using a + or - for the second derivative chart and use them to determine where f(x) is concave up/down. (-4,4) (4/3,00) (4,00) c) Determine the equations for Vertical/Horzontal Asymptotes co-ordinates of
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:3.
A function and its first 2 derivatives are given.
x² - 4x
(x+4)²
f(x)=
(x + 4)³
(3x - 4)
f'(x)
f(x) ↑ or ↓?
ƒ'(x) =
=
-24(x-4)
(x + 4) 4
f"(x)
f(x) CU or CD ?
4(3x-4)
(x+4)³
a) Complete the table below using a + or
them to determine where f(x) is increasing/decreasing.
(-∞, -4)
f"(x) = -²4(x-4)
(x+4)4
(-∞, —4)
+
- for the first derivative chart and use
(-4, 4/3)
+
b) Complete the table below using a + or for the second derivative chart and
use them to determine where f(x) is concave up/down.
(-4,4)
(4/3,00)
(4,00)
c) Determine the equations for Vertical/Horzontal Asymptotes, co-oridinates of
local max/mins, and points of inflection.
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