Calculus 171 Quiz Relating to Chapter 3 of Thomas
Name___________________________________
You must show your work on #'s 1 & 2 to receive credit.
Score_______________/10
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find an equation for the line tangent to the given curve at the indicated point.
1) y = x3 - 36x - 1 at (6, -1)
A) y = -1
B) y = 72x - 1
C) y = 72x - 433
D) y = 71x - 433
1)
Show your work:
Use the definition (0 credit if you don't) f'(x) =
2) f(x) = 3x A) 3 -
lim f(x + h) - f(x)
to find the derivative of f at x.
h 0
h
2
x
2
x
2)
B) 3x +
2
x2
C) 3 -
1
x2
D) 3 +
2
x2
Show your work:
Find the derivative of y with respect to x.
2x - 4
3) y =
6x2 + 5
3)
A)
12x3 - 24x2 + 58x
(6x2 + 5)2
B)
-12x2 + 38x + 30
(6x2 + 5)2
C)
-12x2 + 48x + 10
(6x2 + 5)2
D)
36x2 - 48x + 10
(6x2 + 5)2
1
Solve the problem.
4) If f(2) = 7,
A) -
df
dg
d(g/f)
(2) = 3, g(2) = -3,
(2) = -5, find
(2).
dx
dx
dx
26
49
B)
26
49
C) -
5) Find all points on the curve y = cos x, 0 x
A) ( , - 1)
Find dy/dx.
6) y =
B)
2
4)
26
7
D) -
44
49
2 , where the slope of the curve is -1
,0
C)
3
,0
2
D) (2 , 1)
5x + 2 4
x-4
A)
C)
-88
5)
6)
3
5x + 2 3
-88
·
x-4
(x - 4)2
5x + 2 3
22
·
D)
x-4
(x - 4)2
B)
(x - 4)2
5x + 2 3
x-4
Assuming that the equation defines a differentiable function y of x, find dy/dx by implicit differentiation.
7) cos (xy) + x4 = y4
4x3 + y sin xy
4x3 - x sin xy
4x3 - y sin xy
4x3 + x sin xy
A)
B)
C)
D)
4y3 - x sin xy
4y3
4y3 + x sin xy
4y3
Use logarithmic differentiation to find the derivative of y.
8) y = (x4 + 1)5(x - 1)2 x4
A) (x4 + 1)5 (x - 1)2x4(5ln(x4 + 1) + 2ln(x - 1) + 4ln x)
7)
8)
20x3
2
4
+
+
B) (x4 + 1)5 (x - 1)2x4
x4 + 1 x - 1 x
C)
20x3
2
4
+
+
4
x
1
x
x +1
24
2
+
D) (x4 + 1)5 (x - 1)2x4
x
x-1
Find
dy
.
dx
9) sin y = 5x + 2y
1
A)
sin y - 2
5+2
C)
cos y
B) 5 + 2 - cos y
5
D)
cos y - 2
Use logarithmic differentiation to find the derivative of y with respect to the independent variable.
10) y = xln x
2 ln x
A) 2xln x - 1ln x
B)
C) xln x - 1ln x
D) ln x 2
x
2
9)
10)