POWERPOINT JEOPARDY...Title POWERPOINT JEOPARDY Author Educational Technology Network Subject Jeopardy Template Keywords Jeopardy Powerpoint Template;Educational Technology Created
Post on 07-Oct-2020
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Tangent Lines
ApplicationsLimit
DefinitionPower RuleMiscellaneous
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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
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