find the equation of The Tangent-Line for given function 𝑓(π‘₯) at a given π‘₯ = 𝑐. 50) 𝑓(π‘₯) = π‘₯2 βˆ’ 3π‘₯ + 2 ; π‘Žπ‘‘ π‘₯ = 1

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

MAC 2233 Homework 3 Spring 2021

Name___________________________________

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

ο‚· For each problem from problem 41) to 49), given 𝒇(𝒙) compute

it derivative function 𝒇 β€²(𝒙) .

41) 𝑓(π‘₯) = 2βˆ’π‘₯2

3π‘₯2+1

 

 

 

 

 

 

42) 𝑓(π‘₯) = (π‘₯3 + 2π‘₯ βˆ’ 7)(3 + π‘₯ βˆ’ π‘₯2 )

 

 

 

 

 

43) 𝑓(π‘₯) = √π‘₯2 + 1

 

 

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

44) 𝑓(π‘₯) = (π‘₯ + 1

π‘₯ )

2 βˆ’

5

√3π‘₯

 

 

 

 

 

 

 

 

 

 

45) 𝑓(π‘₯) = (5π‘₯ 4 βˆ’ 3π‘₯ 2 + 2π‘₯ + 1)10

 

 

 

 

46) 𝑓(π‘₯) = ( π‘₯+1

1βˆ’π‘₯ )

2

 

 

 

47) 𝑓(π‘₯) = (3π‘₯ + 1)√6π‘₯ + 5

 

 

 

 

 

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

48) 𝑓(π‘₯) = (3π‘₯+1)3

(1βˆ’3π‘₯)4

 

 

49) 𝑓(π‘₯) = √ 1βˆ’2π‘₯

3π‘₯+2

 

ο‚· From problem 50) to 52) find the equation of The Tangent-Line for given function 𝑓(π‘₯) at a given π‘₯ = 𝑐.

50) 𝑓(π‘₯) = π‘₯2 βˆ’ 3π‘₯ + 2 ; π‘Žπ‘‘ π‘₯ = 1

 

 

 

 

 

 

 

 

 

 

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

51) 𝑓(π‘₯) = π‘₯

x2+1 ; π‘Žπ‘‘ π‘₯ = 0

 

 

 

 

 

 

 

 

52) 𝑓(π‘₯) = √π‘₯2 + 5 ; π‘Žπ‘‘ π‘₯ = βˆ’2

 

 

 

 

 

 

 

ο‚· 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(𝑑) = 2𝑑 2βˆ’5

1βˆ’3t ; π‘Žπ‘‘ 𝑑 = βˆ’1

 

 

 

 

 

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

54) 𝑓(𝑑) = ( t2 βˆ’ 3𝑑 + 6 ) 1

2 ; π‘Žπ‘‘ 𝑑 = 1

 

 

 

 

 

 

ο‚· 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(𝑑) = 𝑑 2 βˆ’ 3𝑑 + βˆšπ‘‘ ; π‘Žπ‘‘ 𝑑 = 4

 

 

 

56) 𝑓(𝑑) = 2

1+𝑑 2 ; π‘Žπ‘‘ 𝑑 = 0

 

 

ο‚· For problem 57), 58) and 59)Find the 2nd –derivatives:

57) 𝑓(π‘₯) = 6π‘₯5 βˆ’ 4π‘₯3 + 5π‘₯2 βˆ’ 2π‘₯ + 1

π‘₯

 

 

 

 

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

58) 𝑓(π‘₯) = 2

1+π‘₯2

 

 

 

 

59) 𝑓(π‘₯) = (3π‘₯2 + 2)4

 

 

 

 

60) For the function 𝑓(π‘₯) given below,

Find the nth-derivative 𝑓(𝑛)(π‘₯) .

 

𝑓(π‘₯) = 1

1βˆ’π‘₯

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