lecture 13 - section 4.5 some max-min problemsjiwenhe/math1431/lectures/lecture13.pdf · jiwen he,...
TRANSCRIPT
Section 4.5
Lecture 13Section 4.5 Some Max-Min Problems
Jiwen He
Department of Mathematics, University of Houston
[email protected]/∼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
Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 18 / 20
Section 4.5
Example 5
Jiwen He, University of Houston Math 1431 – Section 24076, Lecture 13 October 14, 2008 19 / 20