Section 4.5

Lecture 13Section 4.5 Some Max-Min Problems

Jiwen He

Department of Mathematics, University of Houston

jiwenhe@math.uh.edumath.uh.edu/∼jiwenhe/Math1431

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 1 / 20

Section 4.5

Test 1

The written questions on Test 1 have been graded onMonday, and should appear as a separate column in yourCourseWare gradebook by Wednesday.

You will have to add the two columns to get your total scoreon the exam.

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 2 / 20

Section 4.5

Quiz 1

Assume the domain of f is all real numbers. The graph of f ′(x) isshown below. Give the number of critical values of f .

a. 2

b. 3

c. 4

d. 5

e. None of these

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 3 / 20

Section 4.5

Quiz 2

Assume the domain of f is all real numbers. The graph of f ′(x) isshown below. Give the number of local minima of f .

a. 1

b. 2

c. 3

d. 4

e. None of these

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 4 / 20

Section 4.5

Quiz 3

Assume the domain of f is all real numbers. The graph of f ′(x) isshown below. Give the number of local maxima of f .

a. 1

b. 2

c. 3

d. 4

e. None of these

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 5 / 20

Section 4.5

Quiz 4

Assume the domain of f is all real numbers. The graph of f ′(x) isshown below. Give the number of intervals of increase of f .

a. 1

b. 2

c. 3

d. 4

e. None of these

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 6 / 20

Section 4.5

Quiz 5

Assume the domain of f is all real numbers. The graph of f ′(x) isshown below. Give the number of intervals of decrease of f .

a. 1

b. 2

c. 3

d. 4

e. None of these

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 7 / 20

Section 4.5

Quiz 6

Assume the domain of f is all real numbers. The graph of f ′(x) isshown below. Classify the critical value at −3 or state that thevalue is not a critical value.

a. local maximum

b. local minimum

c. neither

d. not a critical value

e. None of these

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 8 / 20

Section 4.5

Quiz 7

Assume the domain of f is all real numbers. The graph of f ′(x) isshown below. Classify the critical value at −2 or state that thevalue is not a critical value.

a. local maximum

b. local minimum

c. neither

d. not a critical value

e. None of these

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 9 / 20

Section 4.5

Quiz 8

Assume the domain of f is all real numbers. The graph of f ′(x) isshown below. Classify the critical value at −1 or state that thevalue is not a critical value.

a. local maximum

b. local minimum

c. neither

d. not a critical value

e. None of these

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 10 / 20

Section 4.5

Quiz 9

Assume the domain of f is all real numbers. The graph of f ′(x) isshown below. Classify the critical value at 0 or state that the valueis not a critical value.

a. local maximum

b. local minimum

c. neither

d. not a critical value

e. None of these

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 11 / 20

Section 4.5

Quiz 10

Assume the domain of f is all real numbers. The graph of f ′(x) isshown below. Classify the critical value at 1 or state that the valueis not a critical value.

a. local maximum

b. local minimum

c. neither

d. not a critical value

e. None of these

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 12 / 20

Section 4.5

Quiz 11

Assume the domain of f is all real numbers. The graph of f ′(x) isshown below. Classify the critical value at 2 or state that the valueis not a critical value.

a. local maximum

b. local minimum

c. neither

d. not a critical value

e. None of these

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 13 / 20

Section 4.5

Quiz 12

Assume the domain of f is all real numbers. The graph of f ′(x) isshown below. Classify the critical value at 3 or state that the valueis not a critical value.

a. local maximum

b. local minimum

c. neither

d. not a critical value

e. None of these

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 14 / 20

Section 4.5

Example 1

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 15 / 20

Section 4.5

Example 2

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 16 / 20

Section 4.5

Example 3

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 17 / 20

Section 4.5

Example 4

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Section 4.5

Example 5

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Section 4.5

Example 6

Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 20 / 20