Calculus Derivates Review
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Calculus Derivatives Quiz Review Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find Dx y.
1) y = - 6x5
A) - 30x4
2) y = x 8 + e8 A) 8x9 3) y =
B) - 30x5
C) - 30x6
D) - 6x 4
B) 8x8 + 8e8
C) 8x7
D) 8x7 + 8e7
1 10 1 3 x - x 2 3
A) 5x11 - x4
4) y = (6x - 4)(6x + 1) A) 72x - 30
C)
B) 36x - 18
C) 72x - 18
B) 40x 3 - 27x2 + 81x + 2 D) 40x 3 - 81x2 + 10x + 2
D) 72x - 9
4)
5)
6)
7)
7x2 - 8
7 x2 - 14 x - 8 (7x2 - 8)2
C) -
D) 5x10 - x3
B) -56x3 + 63x2 + 10x - 15 D) -56x3 + 63x2 + 10
6) y = (2x - 5)(5x3 - x2 + 1) A) 10x 3 + 27x2 - 81x + 2 C) 30x 3 + 81x2 - 27x + 2
8) y =
1 9 1 2 x - x 2 3
B) 5x9 - x2
C) -56x4 + 63x3 + 10x
A)
2)
3)
5) y = (2x - 3)(5 - 7x3 ) A) -14x3 + 21x2 + 10
7) y =
1)
B) -
14 x (7x2 - 8)2
D)
14 x 7x2 - 8
8 - 14 x (7x2 - 8)2
5x - 8
8)
x2 - 6x + 4
A)
5x 3 - 40x 2 + 66x - 48 (x2 - 6x + 4)2
B)
5x 2 + 16x - 28 x2 - 6x + 4
C)
15x2 - 76x + 68 (x2 - 6x + 4)2
D)
-5x2 + 16x + -28 (x2 - 6x + 4)2
1
Solve the problem. 9) If f(1) = 3, f'(1) = -7, g(1) = 6, g'(1) = -2, find (f/g)'(1) A) - 9
B) - 6
C) - 1
10) If f(1) = 4, f'(1) = -7, g(1) = 6, g'(1) = -4., find (f ยท g)'(1) A) 58 B) -52 C) 26
9)
4 D) 3
10)
D) -58
Find the equation of the tangent line to the equation at the point where x has the given value. 6x ; x=1 11) y = 2 x +1 A) y = 0
B) y = 3x
C) y = 3
11)
D) y = x + 3
Solve the problem.
12) At what points on the graph of y = 2x 3 - 3x2 - 34x is the slope of the tangent line 2? A) (-2, 40), (1, -35) B) (0, 0), (3, -75) C) (2, -64), (40, 21) D) (-2, 40), (3, -75)
12)
13) For what value of x is the slope of a line tangent to the curve of y = 17x - x2 equal to the slope of a 1 line tangent to the curve of y = 16x - x2 ? 2
13)
A) x = -1
B) x = 8
C) x = 1
D) x = 0
Find f (x) for the following function. 14) f(x) = 5x -3 + 8x-2 + 9x
14)
A) -15x-4 - 16x-3 + 9 C) 60x -5 + 48x -4 15) f(x) =
B) 60x -5 + 48x -4 + 9 D) -60x-4 - 48x-3
8 x-2
A) -
8
(x - 2)2
15) B)
8 (x - 2)3
C)
2
16 (x - 2)3
D) -
16
(x - 2)3
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find Dx y.
1) y = - 6x5
A) - 30x4
2) y = x 8 + e8 A) 8x9 3) y =
B) - 30x5
C) - 30x6
D) - 6x 4
B) 8x8 + 8e8
C) 8x7
D) 8x7 + 8e7
1 10 1 3 x - x 2 3
A) 5x11 - x4
4) y = (6x - 4)(6x + 1) A) 72x - 30
C)
B) 36x - 18
C) 72x - 18
B) 40x 3 - 27x2 + 81x + 2 D) 40x 3 - 81x2 + 10x + 2
D) 72x - 9
4)
5)
6)
7)
7x2 - 8
7 x2 - 14 x - 8 (7x2 - 8)2
C) -
D) 5x10 - x3
B) -56x3 + 63x2 + 10x - 15 D) -56x3 + 63x2 + 10
6) y = (2x - 5)(5x3 - x2 + 1) A) 10x 3 + 27x2 - 81x + 2 C) 30x 3 + 81x2 - 27x + 2
8) y =
1 9 1 2 x - x 2 3
B) 5x9 - x2
C) -56x4 + 63x3 + 10x
A)
2)
3)
5) y = (2x - 3)(5 - 7x3 ) A) -14x3 + 21x2 + 10
7) y =
1)
B) -
14 x (7x2 - 8)2
D)
14 x 7x2 - 8
8 - 14 x (7x2 - 8)2
5x - 8
8)
x2 - 6x + 4
A)
5x 3 - 40x 2 + 66x - 48 (x2 - 6x + 4)2
B)
5x 2 + 16x - 28 x2 - 6x + 4
C)
15x2 - 76x + 68 (x2 - 6x + 4)2
D)
-5x2 + 16x + -28 (x2 - 6x + 4)2
1
Solve the problem. 9) If f(1) = 3, f'(1) = -7, g(1) = 6, g'(1) = -2, find (f/g)'(1) A) - 9
B) - 6
C) - 1
10) If f(1) = 4, f'(1) = -7, g(1) = 6, g'(1) = -4., find (f ยท g)'(1) A) 58 B) -52 C) 26
9)
4 D) 3
10)
D) -58
Find the equation of the tangent line to the equation at the point where x has the given value. 6x ; x=1 11) y = 2 x +1 A) y = 0
B) y = 3x
C) y = 3
11)
D) y = x + 3
Solve the problem.
12) At what points on the graph of y = 2x 3 - 3x2 - 34x is the slope of the tangent line 2? A) (-2, 40), (1, -35) B) (0, 0), (3, -75) C) (2, -64), (40, 21) D) (-2, 40), (3, -75)
12)
13) For what value of x is the slope of a line tangent to the curve of y = 17x - x2 equal to the slope of a 1 line tangent to the curve of y = 16x - x2 ? 2
13)
A) x = -1
B) x = 8
C) x = 1
D) x = 0
Find f (x) for the following function. 14) f(x) = 5x -3 + 8x-2 + 9x
14)
A) -15x-4 - 16x-3 + 9 C) 60x -5 + 48x -4 15) f(x) =
B) 60x -5 + 48x -4 + 9 D) -60x-4 - 48x-3
8 x-2
A) -
8
(x - 2)2
15) B)
8 (x - 2)3
C)
2
16 (x - 2)3
D) -
16
(x - 2)3
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