Let f(x)=e^(6x)-kx, for k>0 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^2y/dk^2 to use the second derivative test (d^2y)/(dk^2)=
Let f(x)=e^(6x)-kx, for k>0 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^2y/dk^2 to use the second derivative test (d^2y)/(dk^2)=
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let f(x)=e^(6x)-kx, for k>0
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
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^2y/dk^2 to use the second derivative test
(d^2y)/(dk^2)=
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