Using a calculator or computer, sketch the graph of f for k = 1/9, 1/6, 1/3, 1/2, 1, 2, 4. Describe what happens as k changes. f(x) has a local minimum. Find the location of the minimum. x = Find the y-coordinate of the minimum. y = Find the value of k for which this y-coordinate is largest. k = How do you know that this value of k maximizes the y-coordinate? Find d' yldk? to use the second-derivative test. dy (Note that the derivative you get is negative for all positive values of k, and confirm that you agree that this means that your value of k maximizes the y-coordinate of the minimum.)
Using a calculator or computer, sketch the graph of f for k = 1/9, 1/6, 1/3, 1/2, 1, 2, 4. Describe what happens as k changes. f(x) has a local minimum. Find the location of the minimum. x = Find the y-coordinate of the minimum. y = Find the value of k for which this y-coordinate is largest. k = How do you know that this value of k maximizes the y-coordinate? Find d' yldk? to use the second-derivative test. dy (Note that the derivative you get is negative for all positive values of k, and confirm that you agree that this means that your value of k maximizes the y-coordinate of the minimum.)
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:Using a calculator or computer, sketch the graph of f for k = 1/9, 1/6, 1/3, 1/2, 1, 2, 4. Describe what happens as k changes.
%3D
f(x) has a local minimum. Find the location of the minimum.
X =
Find the y-coordinate of the minimum.
y =
Find the value of k for which this y-coordinate is largest.
k =
How do you know that this value of k maximizes the y-coordinate? Find d² yldk2 to use the second-derivative test.
dy
dk
(Note that the derivative you get is negative for all positive values of k, and confirm that you agree that this means that your value of k
maximizes the y-coordinate of the minimum.)
Transcribed Image Text:Let f(x) = e5x – kx, for k > 0.
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