Calculus Assignments

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
 For each problem from problem 41) to 49), given 𝒇(𝒙) compute
it derivative function 𝒇 ′(𝒙) .
41) 𝑓(𝑥) =
2−𝑥
2
3𝑥
2+1
42) 𝑓(𝑥) = (𝑥
3 + 2𝑥 − 7)(3 + 𝑥 − 𝑥
2
)
43) 𝑓(𝑥) = √𝑥
2 + 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) = 𝑥
2 − 3𝑥 + 2 ; 𝑎𝑡 𝑥 = 1
MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE
MAC 2233 SPRING 2021
51) 𝑓(𝑥) =
𝑥
x
2+1
; 𝑎𝑡 𝑥 = 0
52) 𝑓(𝑥) = √𝑥
2 + 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) = ( t
2 − 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) = 6𝑥
5 − 4𝑥
3 + 5𝑥
2 − 2𝑥 +
1
𝑥
MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE
MAC 2233 SPRING 2021
58) 𝑓(𝑥) =
2
1+𝑥
2
59) 𝑓(𝑥) = (3𝑥
2 + 2)
4
60) For the function 𝑓(𝑥) given below,
Find the nth-derivative 𝑓
(𝑛)(𝑥) .
𝑓(𝑥) =
1
1−𝑥