Download Calculus 1 Worksheet #14 Derivative Review For #1 and 2, use the

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Calculus 1 Worksheet #14
Derivative Review
f ( a + h) − f ( a )
For #1 and 2, use the definition f '(a) = lim
to find derivative of the given function at the
h →0
h
indicated point.
−9
9
11 121
9
A)
B) C)
D)
f(x)= ,a =-11
x
11
9
9
121
f(x)=x3+6, a=2
A) -12 B) 13 C) 18 D) 12
For #3-6, find the slope of the line tangent to the curve at the given value of x.
y = x2-9x; x=-5
A) 70
B) -10
C) -19
D) 35
2
If y=x +3, find the equation of the tangent line to the graph of y at x=4.
A) y=8x-13
B) y=8x-29
C) y=4x-13
D) y=8x-26
2
Find an equation of the tangent line to the graph of y=x-x at the point (-2, -6).
A) y=-3x-4
B) y=5x+4
C) y=-3x+4
D) y=-5x+4
2
Find the equation of the normal line to the curve of y=3x-5x at the point (-3,-54).
A) x-27y+975 =0
B)x+33y+1785=0
C)x-27y+1785=0
D)x+33y+975=0
For #7 and 8, solve the problem.
dy
if y=24-3x.
Find
dx
dy
dy
dy
dy
A)
=24-3x
B)
=-3x
C)
=-3
D)
=21
dx
dx
dx
dx
d 2
(x -1).
Find
dx
A) x-1
B)2x-1
C)2x
D)2x2
dy
.
For #9-18, find
dx
1
y=
7 − 4x
A) −
2
7 − 4x
10 y= 19x − x 7
19 − 7 x 6
A)
2 19 x − x 7
11 y=(3x-4)(5x+1)
A) 15x-17
12 y=(6x+3)2
A) 72x+36
13 y=3x4+2x3-8
A) 12x3+6x2
14
1
1
y= x8 − x 4
2
4
A) 4x8-x4
1
B) −
2(7 − 4 x)
B)
1
2 19x − x
7
3
2
C)
C)
7 − 4x
2
D)
3
2(7 − 4 x) 2
−7 x 6
2 19 x − x
1
7
D)
1
2 19 − 7x 6
B) 30x-23
C) 30x-17
D) 30x-8.5
B) 36x+9
C) 36x+18
D) 12x+6
B) 4x3+3x2
C) 12x3+6x2-7
D) 4x3+3x2-7
B) 4x7-x3
C)
1 7 1 3
x − x
2
4
D) 4x9-x5
15
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Calculus 1 Worksheet #14
Derivative Review
7x + 3
6x − 2
84 x + 4
A)
6x − 2
y=
B) −
32
(6 x − 2) 2
C) −
x2
6 − 8x
−24 x 2 + 12 x
8 x 3 − 16 x 2 + 12 x
A)
B)
(6 − 8 x) 2
(6 − 8 x) 2
y=10x-2+8x3-6x
A) 20x-3+24x2
B) -20x-1+24x2-6
x −8
y=
x +8
16
8
B)
A)
x ( x + 8) 2
( x + 8) x − 64
Find the fourth derivative of the function.
y= 6x5-5x2-6x+1
A) 720
B) 480x2+10
Determine the limit by substitution.
lim( x 3 + 5 x 2 − 7 x + 1)
32 x
(6 x − 2) 2
D)
4
6x − 2
D)
−8 x 2 + 12 x
(6 − 8 x) 2
y=
C)
6x
(6 − 8 x) 2
C) -20x-1+24x2
C) −
D) -20x-3+24x2-6
8
x ( x + 8) 2
D)
C) 480x+10
8
x +8
D) 360x
x →2
A) 15
B)Does not exists
21 Determine the limit algebraically if it exists.
lim x − 3
C) 0
D) 29
A) 1
B)Does not exists
22 Determine the limit algebraically if it exists.
x2 − 4
lim
x →−2 x + 2
A) -4
B) 1
C) -1
D) 0
C) -2
D) Does not exists
x →2
Answers:
1 D
2 D
12 A
13 A
3 C
14 B
4 A
15 B
5 B
16 D
6 B
17 D
7 C
18 B
8 C
19 A
9 D
20 A
10 A
21 B
11 C
22 A