Question #2 ( a) Given the sketch of the following function segment, what are the signs of the first and second derivatives? The first derivative is The second derivative is b) Now sketch a function segment that has negative first derivative and positive second derivative. c) If for a given function at point x=a, the first derivative is f'(a) = 0 and the second derivative is f"(a) =1, then what term from class (e.g. intercept, asymptote, local or global maximum, inflection point,etc) best describes this point on the function graph: Answer: d) For another function, a student correctly finds a critical point at x=3 and then correctly calculates that f"(3)=0. The student concludes that x=3 is not a local extremum. Do you agree or disagree with the student's conclusion? Justify with a brief explanation.
Question #2 ( a) Given the sketch of the following function segment, what are the signs of the first and second derivatives? The first derivative is The second derivative is b) Now sketch a function segment that has negative first derivative and positive second derivative. c) If for a given function at point x=a, the first derivative is f'(a) = 0 and the second derivative is f"(a) =1, then what term from class (e.g. intercept, asymptote, local or global maximum, inflection point,etc) best describes this point on the function graph: Answer: d) For another function, a student correctly finds a critical point at x=3 and then correctly calculates that f"(3)=0. The student concludes that x=3 is not a local extremum. Do you agree or disagree with the student's conclusion? Justify with a brief explanation.
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:Question #2 (
a) Given the sketch of the following function segment,
what are the signs of the first and second
derivatives?
The first derivative is
The second derivative is
b) Now sketch a function segment that has negative first
derivative and positive second derivative.
c) If for a given function at point x=a, the first derivative is f"(a) = 0 and the second
derivative is f"(a)=1, then what term from class (e.g. intercept, asymptote, local or
global maximum, inflection point,etc) best describes this point on the function graph:
Answer:
d) For another function, a student correctly finds a critical point at x=3 and then correctly
calculates that f"(3) = 0. The student concludes that x=3 is not a local extremum.
Do you agree or disagree with the student's conclusion? Justify with a brief explanation.
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