Calculus Assignments

MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING 2021

MAC 2233 Homework 4 Spring 2021

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Show all work in the space provided. If no work is shown, the problem

will receive at most half credit for a correct answer.

❖ Application of 𝒇 ′(𝒙) to find the graph of 𝒇(𝒙)

• For problems 61) through 64) Find the intervals of increase and

decrease for each given function 𝑓(𝑥)

61) 𝑓(𝑥) = 1

3 𝑥 3 − 9𝑥 + 2

62) 𝑓(𝑥) = 𝑥2

𝑥−3

MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING 2021

63) 𝑓(𝑥) = 1

16−𝑥2

64) 𝑓(𝑥) = 𝑥 2 + 1

𝑥2

• For problems 65) through 69) determine the critical-numbers 𝒙 = 𝒄 of each of the given function 𝑓(𝑥) and classify each

critical-point ( 𝑐 , 𝑓(𝑐) ) as a Local-Maximum, Local-Minimum, or neither:

65) 𝑓(𝑥) = 3𝑥 4 − 8𝑥 3 + 6𝑥 2 + 2

MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING 2021

66) 𝑓(𝑥) = 2𝑥 3 + 6𝑥 2 + 6𝑥 + 5

67) 𝑓(𝑥) = 𝑥2

𝑥−1

68) 𝑓(𝑥) = 3 + (𝑥 2 − 2𝑥 − 3) 2

5

MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING 2021

69) 𝑓(𝑥) = 𝑥√9 − 𝑥

70) Find constants 𝑎 , 𝑏 and 𝑐 so that the graph of the function 𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 has a Local-Maximum at (5, 12) and crosses the y-axis at (0, 3).

MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING 2021

• For problems 71) through 73) determine the intervals of concavity

and classify each of these intervals as concave-up and concave-

down for each of the given function 𝑓(𝑥). Also, find all the inflection-points ( if any).

71) 𝑓(𝑥) = 2𝑥 6 − 5𝑥 4 + 7𝑥 − 3

72) 𝑓(𝑥) = 𝑥 2 − 1

𝑥

73) 𝑓(𝑥) = (𝑥 − 4) 7

3

MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING 2021

• [PUTTING PIECES TOGETHER…]

For problems 74) through 76) for each given function

𝑓(𝑥) determine a) Find intervals on which 𝑓(𝑥) increasing and decreasing. b) Find intervals on which the graph of 𝑓(𝑥) is concave-up

and concave-down. c) Find all critical-numbers and classify them as

Local-maximum, Local-Minimum or neither.

d) Find all the inflection-points of 𝑓(𝑥) ( if any). 74) 𝑓(𝑥) = 𝑥 4 − 4𝑥 3 + 10

75) 𝑓(𝑥) = (𝑥 2 − 5)3

MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING 2021

76) 𝑓(𝑥) = 𝑥 4 + 6𝑥 3 − 24𝑥 2 + 24

• For problems 77) through 80) for each given function 𝑓(𝑥) Find the Critical-Points and use the Second-Derivative-Test

To find Local-Maximum and Local-Minimum of the given

𝑓(𝑥) .

77) 𝑓(𝑥) = 𝑥 4 − 2𝑥 3 + 3

78) 𝑓(𝑥) = 2𝑥 + 1 + 18

𝑥

MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING 2021

79) 𝑓(𝑥) = ( 𝑥

𝑥+1 )

2

80) 𝑓(𝑥) = (𝑥+3)3

(𝑥−1)2