antiderivatives lesson 7.1b down with derivatives
TRANSCRIPT
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Antiderivatives
Lesson 7.1B
Downwith
Derivatives
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ApplicationsSuppose you know an expression for the marginal revenue• That is the rate at which the revenue is increasing or
decreasing
How can you find the revenue function?
Given
The marginal revenue is the derivative of the revenue function• We seek the antiderivative of the marginal revenue
2
230 4dR
x xdx
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Finding the Demand Function
Then
Now R(0) = 0 so C = 0• And
Revenue = x • Demand• So
3
3
2 230 4 30 2 ( )3
xx x dx x x C R x
32( ) 30 23
xR x x x
2
( ) 30 23
xD x x
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Velocity and Acceleration
Recall relationship of s(t), v(t), and a(t)• v(t) = s '(t)• a(t) = v '(t) = s ''(t)
Given• v(0) = 6• Determine v(t)
4
2( ) 1a t t
2 1t dt3
( )3
tt C v t
(0) 0 0 6
6
v C
C
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Given the Slope Function
Can you find the original function?
Given • And the original function goes through (1, 1)• Find the original function
5
2'( ) 9 5f x x
2 39 5 3 5 ( )x dx x x C f x 33 1 5 1 1
3
C
C
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Assignment
Lesson 7.1B
Page 439
Exercises 45 – 71 odd
6