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1.
y
Answer true or false. If
A) True
B) False
2.
y
If
A)
B)
C)
D)
E)
3.
dy
6x
x  12 , find dx
3
1
1
y' 
2x  2 ,
2 .
.
8
9
8
9
6

9
6
9


y
8
225
3
x  9 , y '(2) 
If
A) 0
B)
3
121
C)
27

121
D)
3

121
E)
9

121
4. g(x) = x2f(x). Find g(4), given that f(4) = 4 and f (4) = 7.
A) 120
B) 48
C) 144
D) 240
E) 56
Page 1
5. Answer true or false. If f, g, and h are differentiable functions, and h  0 anywhere on its
 fg  fhg ' ghf ' fgh '
  
h2
domain, then  h 
.
A) True
B) False
6.
If
A)
B)
C)
D)
E)
7.
1
x  6 , find y(25) .
y

1
6
1
6
1
10
1
25
1

10




dy
5 x 2  2 x 6  x7
dx
Find
if y =
.
8.
f ( x) 
Find f '(x) if
6 x2  1
2 x2  5x .
9. If f(3) = 3, f (3) = 3, g(3) = 3, g (3) = –2, find F(3) if F(x) = 4f(x) - 2g(x) .
10. If f(6) = 3, f (6) = 5, g(6) = 3, g (6) = 4, find F(6) if F(x) = 2 f ( x ) g ( x ) .
11.
3 f ( x)
If f(5) = 18, f (5) = –2, g(5) = 3, g (5) = 0, find F(5) if F(x) = g ( x) .
Page 2
12.
f (u ) 
Find f '(u) if
13.
f (t ) 
Find f '(t) if
14.
u2  2
2u 2  5 .
2t 4  6t 3
2t 5
.
dy
Find dx if y = (x2 - 3)(x3 + 4x).
15. Find f '(x) if f(x) = (x2 + 3)(x3 - 4x2 + x).
16.
y
Find the equations of the tangent and normal to the graph of
Page 3
x 1
x  1 at x = 12.
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
B
B
D
C
A
E
dy
 5  2 x  2  6  x 7  35 x 6 x 2  2 x
dx



 = 15x - 48x + 6x - 12
12 x  2 x  5 x    4 x  5   6 x  1
30 x 2  4 x  5
f '( x) 
2
2 x2  5x 
 2 x  5x 

=
2
2
9. 16
10. 108
11. 9
1
4
2
- 2 of
12.
2u 2u 2  5  4u u 2  2
f '(u ) 
2
2u 2  5
-1


-2


-2

 

–2u
 2u
=
2
5

2
-3
13. y = t - 4t
So y' = -t + 8t .
14. dy
 2 x x3  7 x  3 x 2  7 x 2  4
dx
15. f '(x) = 5x4 - 16x3 + 12x2 - 24x + 3
16.
2
23

Tangent line: y = 9 x + 9
9
49
Normal line: y = 2 x - 3

3
2
2

4

=
Page 4
5x4 + 3x2 - 12