## Transcribed Text

1) y = x2 + 4x, [4, 7]
A) 11 B) 45
7
C) 77
3
D) 15
1)
2) y = 2x, [2, 8]
A) -
3
10
B) 1
3
C) 7 D) 2
2)
Use the slopes of UQ, UR, US, and UT to estimate the rate of change of y at the specified value of x.
3) x = 5
1 2 3 4 5 6 x
y
5
4
3
2
1
Q
R
S
T
U
1 2 3 4 5 6 x
y
5
4
3
2
1
Q
R
S
T
U
A) 1 B) 2 C) 5 D) 0
3)
Use the table to estimate the rate of change of y at the specified value of x.
4) x = 1.
x y
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0
0.02
0.08
0.18
0.32
0.5
0.72
0.98
A) 2 B) 0.5 C) 1 D) 1.5
4)
Use the graph to evaluate the limit.
5) lim
x→-1
f(x)
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x
y
1
-1
A) 3
4
B) ∞ C) -1 D) -
3
4
5)
Find the limit.
6) lim
x→2
(8x + 3)
A) 3 B) -13 C) 11 D) 19
6)
1) y =
x3
2
, (8, 256)
A) y = 32x - 512 B) y = 32x + 512 C) y = 512x + 96 D) y = 96x - 512
1)
Graph the equation and its tangent.
2) Graph y = 5x2 and the tangent to the curve at the point whose x-coordinate is 1.
-5 5 x
y
10
-10
-5 5 x
y
10
-10
A)
-5 5 x
y
10
-10
-5 5 x
y
10
-10
B)
-5 5 x
y
10
-10
-5 5 x
y
10
-10
C)
-5 5 x
y
10
-10
-5 5 x
y
10
-10
D)
-5 5 x
y
10
-10
-5 5 x
y
10
-10
2)
Calculate the derivative of the function. Then find the value of the derivative as specified.
3) f(x) = 5x + 9; f ′
(2)
A) f ′
(x) = 5; f ′
(2) = 5 B) f ′
(x) = 0; f ′
(2) = 0
C) f ′
(x) = 9; f ′
(2) = 9 D) f ′
(x) = 5x; f ′
(2) = 10
3)
4) g(x) = 3x2 - 4x; g ′
(3)
A) g ′
(x) = 6x; g ′
(3) = 18 B) g ′
(x) = 3x - 4; g ′
(3) = 5
C) g ′
(x) = 2x- 4; g ′
(3) = 2 D) g ′
(x) = 6x - 4; g ′
(3) = 14
4)
Find the indicated derivative.
5) dy
dx
if y = 3x3
A) 9x B) 3x2 C) 9x2 D) 9x3
5)
1) y = 14 - 12x2
A) 14 - 12x B) 14 - 24x C) -24x D) -24
1)
2) y = 5x4 + 7x3 - 4
A) 20x3 + 21x2 B) 4x3 + 3x2 - 7
C) 4x3 + 3x2 D) 20x3 + 21x2 - 7
2)
Find the second derivative.
3) y = 9x2 + 3x - 7
A) 18x + 3 B) 9 C) 18 D) 0
3)
4) y = 6x4 - 7x2 + 2
A) 24x2 - 14x B) 72x2 - 14x C) 72x2 - 14 D) 24x2 - 14
4)
Find y ′
.
5) y = (5x - 5)(6x + 1)
A) 60x - 12.5 B) 60x - 35 C) 30x - 25 D) 60x - 25
5)
Find the derivative of the function.
6) y =
x2 - 3x + 2
x7 - 2
A) y ′ =
-5x8 + 18x7 - 14x6 - 4x + 6
(x7 - 2)2
B) y ′ =
-5x8 + 18x7 - 14x6 - 3x + 6
(x7 - 2)2
C) y ′ =
-5x8 + 18x7 - 13x6 - 4x + 6
(x7 - 2)2
D) y ′ =
-5x8 + 19x7 - 14x6 - 4x + 6
(x7 - 2)2
6)
1) y = x2 + 4x, [4, 7]
A) 11 B) 15 C) 45
7
D) 77
3
1)
Find the slope of the curve at the given point P and an equation of the tangent line at P.
2) y = x2 + 5x, P(4, 36)
A) slope is -
4
25
; y = -
4x
25
+
8
5
B) slope is 13; y = 13x - 16
C) slope is 1
20
; y =
x
20
+
1
5
D) slope is -39; y = -39x - 80
2)
Use the slopes of UQ, UR, US, and UT to estimate the rate of change of y at the specified value of x.
3) x = 5
1 2 3 4 5 6 x
y
5
4
3
2
1
Q
R
S
T
U
1 2 3 4 5 6 x
y
5
4
3
2
1
Q
R
S
T
U
A) 5 B) 0 C) 1 D) 2
3)
Use the table to estimate the rate of change of y at the specified value of x.
4) x = 1.
x y
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0
0.02
0.08
0.18
0.32
0.5
0.72
0.98
A) 1 B) 1.5 C) 0.5 D) 2
4)
1
Use the graph to evaluate the limit.
5) lim
x→-1
f(x)
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x
y
1
-1
A) -
3
4
B) -1 C) 3
4
D) ∞
5)
Find the limit.
6) lim
x→2
(8x + 3)
A) 19 B) 3 C) -13 D) 11
6)
Find the limit if it exists.
7) lim
x→-3
(4x - 4)
A) -16 B) 16 C) 8 D) -8
7)
Find the limit.
8) lim
x→0
(3 sin x - 1)
A) 3 B) 0 C) -1 D) 3 - 1
8)
Find an equation for the tangent to the curve at the given point.
9) y =
x3
2
, (8, 256)
A) y = 32x - 512 B) y = 96x - 512 C) y = 512x + 96 D) y = 32x + 512
9)
Calculate the derivative of the function. Then find the value of the derivative as specified.
10) g(x) = 3x2 - 4x; g ′
(3)
A) g ′
(x) = 6x; g ′
(3) = 18 B) g ′
(x) = 3x - 4; g ′
(3) = 5
C) g ′
(x) = 2x- 4; g ′
(3) = 2 D) g ′
(x) = 6x - 4; g ′
(3) = 14
10)
Find the indicated derivative.
11) dy
dx
if y = 3x3
A) 9x3 B) 3x2 C) 9x2 D) 9x
11)
Find the derivative.
12) y = 2 - 8x3
A) -24x B) 2 - 24x2 C) -16x2 D) -24x2
12)
Find y ′
.
13) y = (5x - 5)(6x + 1)
A) 60x - 12.5 B) 60x - 25 C) 30x - 25 D) 60x - 35
13)
Find the derivative of the function.
14) y =
x3
x - 1
A) y ′ =
-2x3 - 3x2
(x - 1)2
B) y ′ =
2x3 + 3x2
(x - 1)2
C) y ′ =
-2x3 + 3x2
(x - 1)2
D) y ′ =
2x3 - 3x2
(x - 1)2
14)
Find the derivative.
15) y =
8
x
+ 3 sec x
A) y ′ = -
8
x2
+ 3 sec x tan x B) y ′ = -
8
x2
- 3 csc x
C) y ′ =
8
x2
- 3 sec x tan x D) y ′ = -
8
x2
+ 3 tan2x
15)

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