MATH 1325 - ELEMENTS OF CALCULUS
REVIEW 2
L F Thomas - Instructor
Find the derivative of the function.
13) f(x) = (5x - 3)(4x3 - x2 + 1)
SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
Find the derivative.
1) f(x) = 5x4 + 2x3 - 9
14) f(x) = (4x - 3)( x + 2)
15) f(x) = (4x - 4)( x + 2)
2) y = 6x-2 + 6x3 + 13x
Use the quotient rule to find the derivative.
1
16) f(x) =
7
x +2
3) f(x) = 9x7/5 - 5x2 + 104
4) f(x) =
5) y =
4
x; (x > 0)
17) y =
x2 - 4
x
Find the derivative.
(2x + 1)(2x + 2)
18)
2x - 5
Find the following.
6) f'(4) if f(x) = 9x5/2 - 7x3/2
7) f'(4) if f(x) =
7
x
x
19)
x3 - 6
(3x + 3)(5x + 6)
Solve the problem.
20) The total cost to produce x units of perfume is
C(x) = (9x + 6)(9x + 8). Find the marginal
average cost function.
8) f'(1) if f(x) = -x-5 + x-3
Find the equation of the tangent line to the curve when x
has the given value.
9) f(x) = x2 + 11x - 15 ; x = 1
10) f(x) =
x2 - 3x + 2
x7 - 2
Let f(x) = 8x2 - 5x and g(x) = 7x + 9. Find the composite.
21) f[g(3)]
7
;x=3
x-2
Find f[g(x)] and g[f(x)].
22) f(x) = 5x3 + 8; g(x) = 2x
Solve the problem.
11) The profit from the expenditure of x thousand
dollars on advertising is given by
P(x) = 1190 + 15x - 3x2 . Find the marginal
Find the derivative of the function.
23) y = 4x + 2
profit when the expenditure is x = 14.
24) f(x) =
12) The revenue generated by the sale of x bicycles
x2
is given by R(x) = 70.00x . Find the
200
5
(2x - 3)4
25) f(x) = (x3 - 8)2/3
marginal revenue when x = 1300 units.
1
26) f(x) = (6x - 2)(5x + 7)2
Solve the problem.
27) The total number of bacteria (in millions)
present in a culture is given by
N(t) = 4t 6t + 12 - 14 where t represents time
in hours after the beginning of an experiment.
Find the rate of change of the population of
bacteria with respect to time for t = 1.
28) The total revenue from the sale of x stereos is
x 2
given by R(x) = 4000 1 . Find the
400
marginal average revenue.
Find the derivative.
2
29) y = e6x + x
30) y = 5x2 e3x
Find the derivative of the function.
31) y = ln (x - 7)
32) y = ln (4 + x2 )
Find the derivative.
33) f(x) = ln 9 + e10x
Solve the problem.
34) The sales in thousands of a new type of
product are given by S(t) = 200 - 70e-.1t, where
t represents time in years. Find the rate of
change of sales at the time when t = 3.
Find all points where the function is discontinuous.
35)
2
Answer Key
Testname: REVIEW 2 SPR 2015
1) 20x3 + 6x2
2) -12x-3 + 18x2 + 13
3)
63 2/5
- 10x
x
5
4)
1 -3/4
x
4
4
5) y' = 1 +
x2
6) 159
11
7) 16
8) 2
9) y = 13x - 16
10) y = -7x + 28
11) -69 thousand dollars /unit
12) $57.00/unit
13) f'(x) = 80x3 - 51x2 + 6x + 5
14) f'(x) = 6x1/2 - 1.5x-1/2 + 8
15) f'(x) = 6x1/2 - 2x-1/2 + 8
16) f'(x) = 17) y' =
7x6
(x7 + 2)2
-5x8 + 18x7 - 14x6 - 4x + 6
(x7 - 2)2
18)
8x2- 40x - 34
(2x - 5)2
19)
15x4 + 66x3 + 54x2 + 180x + 198
(3x + 3)2 (5x + 6)2
20) 81 -
48
x2
21) 7050
22) f[g(x)] = 40x3 + 8
g[f(x)] = 10x3 + 16
23) y' =
24) f'(x) =
25) f'(x) =
2
4x + 2
-40
(2x - 3)5
2x2
3
x3 - 8
26) f'(x) = 6(5x + 7)2 + 10(6x - 2)(5x + 7)
27) 19.80
3
Answer Key
Testname: REVIEW 2 SPR 2015
28) R'(x) = 0.025 -
4000
x2
2
29) 12xe6x + 1
30) 5xe3x(3x + 2)
31)
1
x-7
32)
2x
2
x +4
33)
10e10x
9 + e10x
34) 5.2 thousand per year
35) x = 1
4