Download Quiz: Graphs and Derivatives, Implicit Differentiation

Quiz: Graphs and Derivatives, Implicit Differentiation, Related Rates
OPEN NOTE (CLOSED BOOK)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
The graph of a function is given. Choose the answer that represents the graph of its derivative.
1)
15
y
10
5
-15 -10
-5
5
15 x
10
-5
-10
-15
A)
B)
15
-15 -10
y
15
10
10
5
5
-5
5
10
15 x
-15 -10
-5
-5
-5
-10
-10
-15
-15
C)
y
5
10
15 x
5
10
15 x
D)
15
-15 -10
y
15
10
10
5
5
-5
5
10
15 x
-15 -10
-5
-5
-5
-10
-10
-15
-15
1
y
1)
′
Given the graph of f, find any values of x at which f is not defined.
2)
A) x = -3, 3
B) x = -2, 0, 2
C) x = -2, 2
2)
D) x = -3, 0, 3
3)
3)
A) x = 1
B) x = 2
C) x = 0, 1, 2
D) x = 0
2
3
4) Suppose that x and y are related by the equation x + y = 4. Use implicit differentiation to
4
2
4)
determine dy .
dx
A)
dy = - 2x
dx
y3
B)
dy = 2y 2
dx
x
C)
dy = - x , y ≠ 0
dx
3y 2
D)
dy = 1 , y ≠ 0
dx 3y 2
5) Suppose that x and y are related by the equation x3 + (2y + 1)2 = y 2. Use implicit differentiation
to determine dy .
dx
A)
dy = 3x2 + 2(y + 1)
dx
B)
dy = 3x2 + 4(2y + 1)
dx
2y
C)
dy = -3x2
dx 2(3y + 2)
D)
dy = -3x2
dx 6y + 1
6) Given 2x2+y 2 = 16, find dy/dt when x = 4 and y = 2.
A) 32
B) -4
C) 4
2
5)
6)
D) -32
Solve the problem. Round your answer, if appropriate.
7) Water is being drained from a container which has the shape of an inverted right circular cone.
The container has a radius of 3.00 inches at the top and a height of 6.00 inches. At the instant
when the water in the container is 5.00 inches deep, the surface level is falling at a rate of 0.5
in./sec. Find the rate at which water is being drained from the container.
A) 16.4 in.3/s
B) 14.4 in.3s
C) 9.37 in.3/s
D) 9.82 in.3/s
8) A man 6 ft tall walks at a rate of 3 ft/sec away from a lamppost that is 17 ft high. At what rate is
the length of his shadow changing when he is 40 ft away from the lamppost? (Do not round
your answer)
A) 18 ft/sec
B) 9 ft/sec
C) 20 ft/sec
D) 18 ft/sec
23
23
11
3
7)
8)