. D11: I can use derivatives to solve optimization problems. (a) Part of the graph of f(x) = x + 2x is given below. i. Does the graph indicate that x = 0 is a critical point? Why/Why not? ii. Use calculus and algebra to find all possible x values where f could possibly change direction (change from increase to decrease or vice versa). Does your algebra indicate that x = 0 is a critical point? Why/Why not? lasitos -2 0 -2 (b) Use the first derivative test to show that f does not have a maximum or a minimum at x = 0. (Hint: you may need to look up this test. Show why it is ok to apply the test to this situation.)
. D11: I can use derivatives to solve optimization problems. (a) Part of the graph of f(x) = x + 2x is given below. i. Does the graph indicate that x = 0 is a critical point? Why/Why not? ii. Use calculus and algebra to find all possible x values where f could possibly change direction (change from increase to decrease or vice versa). Does your algebra indicate that x = 0 is a critical point? Why/Why not? lasitos -2 0 -2 (b) Use the first derivative test to show that f does not have a maximum or a minimum at x = 0. (Hint: you may need to look up this test. Show why it is ok to apply the test to this situation.)
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:4. D11: I can use derivatives to solve optimization problems.
(a) Part of the graph of f(x) = x + 2x is given below.
i. Does the graph indicate that x = 0 is a
critical point? Why/Why not?
ii. Use calculus and algebra to find all
possible x values where f could possibly
change direction (change from increase
to decrease or vice versa). Does your
algebra indicate that x = 0 is a critical
point? Why/Why not?
lasif
(b) Use the first derivative test to show that f does not have a maximum or a minimum at
x = 0. (Hint: you may need to look up this test. Show why it is ok to apply the test to this
situation.)
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VIEWStep 2: Define the critical point at x=0
VIEWStep 3: Calculate the derivative of function
VIEWStep 4: Calculate the critical values
VIEWStep 5: Calculate the sign table
VIEWStep 6: Calculate the increasing and decreasing intervals
VIEWStep 7: Calculate the maximum and minimum at x=0
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