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Max-Min Problems: Identifying Critical Values and Classifying Local Extrema, Exams of Calculus

University of Houston (UH)Calculus

A series of quiz questions related to identifying critical values and classifying local extrema of a function's derivative. Students are required to determine the number of critical values, local minima, local maxima, intervals of increase, and intervals of decrease based on the given graph of the derivative. They are also asked to classify specific critical values as local maxima, local minima, or neither.

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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koofers-user-t2p 🇺🇸

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Lecture 13Section 4.5 Some Max-Min Problems
Jiwen He
Test 1
•The written questions on Test 1 have been graded on Monday, and should
appear as a separate column in your CourseWare gradebook by Wednes-
day.
•You will have to add the two columns to get your total score on the exam.
Quiz 1
Assume the domain of fis all real numbers. The graph of f0(x) is shown
below. Give the number of critical values of f.
a. 2
b. 3
c. 4
d. 5
e. None of these
1
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff

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Lecture 13Section 4.5 Some Max-Min Problems

Jiwen He

Test 1

  • The written questions on Test 1 have been graded on Monday, and should appear as a separate column in your CourseWare gradebook by Wednes- day.
  • You will have to add the two columns to get your total score on the exam.

Quiz 1 Assume the domain of f is all real numbers. The graph of f ′(x) is shown below. Give the number of critical values of f. a. 2 b. 3 c. 4 d. 5 e. None of these

Assume the domain of f is all real numbers. The graph of f ′(x) is shown below. Give the number of local minima of f. a. 1 b. 2 c. 3 d. 4 e. None of these

Assume the domain of f is all real numbers. The graph of f ′(x) is shown below. Give the number of intervals of increase of f. a. 1 b. 2 c. 3 d. 4 e. None of these

Assume the domain of f is all real numbers. The graph of f ′(x) is shown below. Give the number of intervals of decrease of f. a. 1 b. 2 c. 3 d. 4 e. None of these

Assume the domain of f is all real numbers. The graph of f ′(x) is shown below. Classify the critical value at −2 or state that the value is not a critical value. a. local maximum b. local minimum c. neither d. not a critical value e. None of these

Assume the domain of f is all real numbers. The graph of f ′(x) is shown below. Classify the critical value at −1 or state that the value is not a critical value. a. local maximum b. local minimum c. neither d. not a critical value e. None of these

Assume the domain of f is all real numbers. The graph of f ′(x) is shown below. Classify the critical value at 1 or state that the value is not a critical value. a. local maximum b. local minimum c. neither d. not a critical value e. None of these

Assume the domain of f is all real numbers. The graph of f ′(x) is shown below. Classify the critical value at 2 or state that the value is not a critical value. a. local maximum b. local minimum c. neither d. not a critical value e. None of these

1 Section 4.5 Some Max-Min Problems

Example 1

Example 2