Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find dy/dx using implicit differentiation.
1) xy + x + y = x2y2
1) _______
A)
B)
C)
D)
Find an equation for the line tangent to the given curve at the indicated point.
2) x2 + y2 = 25; (-4, 3)
A)
B)
y=-
x+
Differentiate.
3)
y=x
A)
C)
y=
x+
2) _______
D)
y=-
x-
y=
x-
3) _______
B)
=
Find an expression for dy/dx.
4) y =
and u = 3x - 2
A) 18x
C)
=
D)
=
=
4) _______
B) 18x - 12
C) 9x - 6
D) 12x - 6
Differentiate.
5) y =
5) _______
A) (ln x)
6) y =
A)
B) (log 4)
C) (ln 4)
D)
6) _______
x
B)
C)
D)
Find the derivative of y with respect to x.
7)
y=
A)
B)
7) _______
C)
D)
Find the derivative.
8) y = 5x2e3x
A) 5xe3x(2x + 3)
8) _______
B) 10xe3x(2x + 3)
C) 5xe3x(3x + 2)
D) 10ex3x(3x + 2)
Find the value or values of c that satisfy the equation
= f'(c)
in the conclusion of the Mean Value Theorem for the given function and interval.
9) f(x) =
+ 2x + 2, [ -1, 2].
A)
9) _______
B)
-
C)
D)
-1,
2
0,
,
Use l'Hopital's Rule to evaluate the limit.
10)
A) 14
10) ______
B) -7
C) 7
D) -14
Evaluate the definite integral.
11)
11) ______
dx
A)
B)
(
-
)
C) 2(
(
-
)
-
D)
-
)
Evaluate the integral using substitution.
12)
12) ______
dx
A) 7
B)
C) 49
D)
Find the derivative.
13)
y=
A)
13) ______
B)
C)
-
D)
14)
14) ______
y=
A)
B)
Find the domain and the range for the function.
15)
-
C)
D)
15) ______
B) D = (-∞, ∞), R = (-∞, ∞)
D) D = (-4, 8), R = ( -2, 1)
A) D = [-4, 8], R = [ -2, 1]
C) D = {-4, 8}, R = { -2, 1}
Solve the problem.
16) If f(x) = 4x + 14 and g(x) = 2x - 1, find f(g(x)).
A) 8x + 27
B) 8x + 13
16) ______
C) 8x + 18
D) 8x + 10
17)
17) ______
If f(x) =
A)
and g(x) = 9x + 10, find g(f(x)).
B) x
C) x + 20
D) 9x + 80
18) The accompanying figure shows the graph of y =
equation for the new graph.
A) y =
B) y =
-6
shifted to a new position. Write the
C) y =
D) y =
+6
Evaluate using the substitution method.
19)
A) 16 ln
19) ______
B)
+C
ln
D) 16 ln( 4
C)
ln
18) ______
+C
+ 3) + C
+C
20)
20) ______
A) 20 ln
B)
+C
ln
C) 20 ln( 4
+C
D)
+ 8) + C
ln
+C
Find dy/dx using implicit differentiation.
21) 2xy - y2 = 1
A)
B)
21) ______
C)
D)
Use the graph of the function f(x) to locate the local extrema and identify the intervals where the function is concave
up and concave down.
22)
22) ______
A) Local minimum at
on (-∞, 0)
B) Local minimum at
C) Local minimum at
on (-∞, 0)
D) Local minimum at
x = +1; local maximum at x = -1; concave up on (0, ∞); concave down
x = +1; local maximum at x = -1; concave down on (-∞, ∞)
x = +1; local maximum at x = -1; concave down on (0, ∞); concave up
x = +1; local maximum at x = -1; concave up on (-∞, ∞)
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
B
B
D
B
C
B
C
C
A
A
B
D
B
D
A
D
B
B
B
D
A
A