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d. What is the value of limr0 g'(x)? What does the value of this limit tell you about the long-term behavior of g? e. Sketch a possible graph of y = g(x).

d. What is the value of limr0 g'(x)? What does the value of this limit tell you about the long-term behavior of g? e. Sketch a possible graph of y = g(x).

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Can you help me with D and E
Activity 3.1.2. Suppose that g(x) is a function continuous for every value of x # 2 whose first derivative is gʻ(x) = (x+4)(x-1)2 x-2 Further, assume that it is known that g has a vertical asymptote at x = 2. a. Determine all critical numbers of g. b. By developing a carefully labeled first derivative sign chart, decide whether g has as a local maximum, local minimum, or neither at each critical number. c. Does g have a global maximum? global minimum? Justify your claims. d. What is the value of limr→0 gʻ(x)? What does the value of this limit tell you about the long-term behavior of g? e. Sketch a possible graph of y = g(x).
Transcribed Image Text:Activity 3.1.2. Suppose that g(x) is a function continuous for every value of x # 2 whose first derivative is gʻ(x) = (x+4)(x-1)2 x-2 Further, assume that it is known that g has a vertical asymptote at x = 2. a. Determine all critical numbers of g. b. By developing a carefully labeled first derivative sign chart, decide whether g has as a local maximum, local minimum, or neither at each critical number. c. Does g have a global maximum? global minimum? Justify your claims. d. What is the value of limr→0 gʻ(x)? What does the value of this limit tell you about the long-term behavior of g? e. Sketch a possible graph of y = g(x).
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