Antiderivatives

Lesson 7.1B

Downwith

Derivatives

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

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

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

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

Assignment

Lesson 7.1B

Page 439

Exercises 45 – 71 odd

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