Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Tangent Lines
ApplicationsLimit
DefinitionPower RuleMiscellaneous
50
40
30
20
10 10
20
30
40
50
10
20
30
40
50
10
20
30
40
50
10
20
30
40
50
Category 1 – 10 Points
What is the limit definition of
a derivative?
0
( ) ( )limh
f x h f x
h
Category 1 – 20 Points
2
( ) ( ) '( ) ( ) '( ), ( ) 0
( ) ( )
d f x g x f x f x g xg x
dx g x g x
What is the quotient rule?
Category 1 – 30 Points
Find f’(x) if 2x 1
f(x)4x 3
2
4x 3 (2) 2x 1 4
4x 3
2
10
4x 3
Category 1 – 40 Points
Let f(x) = (2x + 3)(x3 + 4)2. Find f’(x)
=(2x + 3)(2(x3 + 4)(3x2)) +(x3 + 4)2(2)
f’(x) = (2x + 3)(6x2 (x3 + 4))+(x3 + 4)2(2)
= (2x + 3)(6x5 + 24x2) + 2(x3 + 4)2
Category 1 – 50 Points
Find f’(x) given that
23
2( )
4f x
x
42 3
4'( )
3( 4)
xf x
x
Category 2 – 10 Points
Find the derivative of
.)( 3 xxf
3/1)( xxf
2/3
3 2
1 1'( )
3 3f x x
x
Category 2 – 20 Points
Find the derivative of
7
3 6( ) 4 6 6f x x x x
1
2 63
'( ) 12 7f x x xx
Category 2 – 30 Points
Find the derivative of
3 4( ) 5f x v v
2
3/4
2
34
1'( ) 15
1'( ) 15
4
4f x
f x
v
v
v
v
Category 2 – 40 Points
Find the derivative of
4 5p(t) 12t 6 t
t
13 2
32
2
3 5p'(t) 48t
p'(t)
tt
48t 3t 5t
Category 2 – 50 Points
Find the derivative of4
3
3 4( )
4 8
xf x
x x
84
4
3 431 x
xx
3
2 4
3 12 1'( )
4 2f x x
x x
Category 3 – 10 Points
Find the derivative using
the limit definition
( ) 7f x
0
Category 3 – 20 Points
Find the derivative using
the limit definition
( ) 2 3f x x
2
Category 3 – 30 Points
Find the derivative using
the limit definition
2( ) 2 3f x x x
2 2x
Category 3 – 40 Points
Find the derivative using
the limit definition
( ) 5f x x
1
2 5x
Category 3 – 50 Points
Find the derivative using
the limit definition
2( )
1f x
x
2
2
( 1)x
Category 4 – 10 Points
What constants are used for
acceleration due to gravity
for ft/sec and m/sec?
2 232 / sec 9.8 / secft and m
Category 4 – 20 Points
Given the position function s = -16t2 + 560, find the velocity
at t = 3.
96 / secft
Category 4 – 30 PointsA rock is shot straight up in the air with a sling
shot. It had a speed of 600m/s. The row is launched with an initial height of 3 m.
What is the equation relating its height as a function of time?
2h(t) 4.9t 600t 3
Category 4 – 40 Points
Find when the velocity
function is at rest.
3 22( ) 6 16 10
3s t t t t
2 4secAt and
Category 4 – 50 Points
The position of a particle is given by s(t) = -16t4 + 18t3 + 50t, where s is the measured in feet and t is measured in seconds. Find the acceleration at t = 3.
21404 / secft
Category 5 – 10 PointsFind the equation of the line
tangent to f(x) = -2x2 + 9x + 1 at x = 3
10 3( 3)
3 19
y x
y x
Category 5 – 20 Points
Find the tangent to the curve
f(x) = 3x2 – 2 at x = 1
1 6( 1)
6 5
y x
y x
Category 5 – 30 Points
Find the derivative at x =14 3( ) 2 4f x x x x
3 2
3 2
24 6
24(1) 6(1)
1
0
x xx
Category 5 – 40 Points
Find the equation of the line
tangent to the given function.
2( ) ( 1)(4 2 1); (3, 12)f x x x x
12 145( 3)
145 447
y x
y x
Category 5 – 50 Points
Find the equation of the line
tangent to the given function in
point slope form.
2
3 1( ) ; 2
2 4
xg x x
x
7 5( 2)
12 36y x
Related Documents
