Calculus Assignments

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

MAC 2233 Homework 3 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.

 Technique and rules to compute the derivative

 For each problem from problem 41) to 49), given 𝒇(𝒙) compute

it derivative function 𝒇 ′(𝒙) .

41) 𝑓(𝑥) = 2−𝑥2

3𝑥2+1

42) 𝑓(𝑥) = (𝑥3 + 2𝑥 − 7)(3 + 𝑥 − 𝑥2 )

43) 𝑓(𝑥) = √𝑥2 + 1

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

44) 𝑓(𝑥) = (𝑥 + 1

𝑥 )

2 −

5

√3𝑥

45) 𝑓(𝑥) = (5𝑥 4 − 3𝑥 2 + 2𝑥 + 1)10

46) 𝑓(𝑥) = ( 𝑥+1

1−𝑥 )

2

47) 𝑓(𝑥) = (3𝑥 + 1)√6𝑥 + 5

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

48) 𝑓(𝑥) = (3𝑥+1)3

(1−3𝑥)4

49) 𝑓(𝑥) = √ 1−2𝑥

3𝑥+2

 From problem 50) to 52) find the equation of The Tangent-Line for given function 𝑓(𝑥) at a given 𝑥 = 𝑐.

50) 𝑓(𝑥) = 𝑥2 − 3𝑥 + 2 ; 𝑎𝑡 𝑥 = 1

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

51) 𝑓(𝑥) = 𝑥

x2+1 ; 𝑎𝑡 𝑥 = 0

52) 𝑓(𝑥) = √𝑥2 + 5 ; 𝑎𝑡 𝑥 = −2

 For problem 53) and 54) Find the rate of change of 𝒇(𝒕)

with respect to 𝒕 at the given value of 𝒕 .

53) 𝑓(𝑡) = 2𝑡 2−5

1−3t ; 𝑎𝑡 𝑡 = −1

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

54) 𝑓(𝑡) = ( t2 − 3𝑡 + 6 ) 1

2 ; 𝑎𝑡 𝑡 = 1

 For problem 55) and 56) Find the Percentage-Rate of

change of 𝒇(𝒕) with respect to 𝒕 at the given value

of 𝒕 .

55) 𝑓(𝑡) = 𝑡 2 − 3𝑡 + √𝑡 ; 𝑎𝑡 𝑡 = 4

56) 𝑓(𝑡) = 2

1+𝑡 2 ; 𝑎𝑡 𝑡 = 0

 For problem 57), 58) and 59)Find the 2nd –derivatives:

57) 𝑓(𝑥) = 6𝑥5 − 4𝑥3 + 5𝑥2 − 2𝑥 + 1

𝑥

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

58) 𝑓(𝑥) = 2

1+𝑥2

59) 𝑓(𝑥) = (3𝑥2 + 2)4

60) For the function 𝑓(𝑥) given below,

Find the nth-derivative 𝑓(𝑛)(𝑥) .

𝑓(𝑥) = 1

1−𝑥