Chapter 5.2, Problem 55E

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Supply In Exercises 53 and 54, find the supply function x   =   f ( p ) that satisfies the initial condition. d x d p  =  6000 p ( p 2   −   16 ) 3 / 2 x  = 5000 when  p   =   $5 To determine To calculate: The demand function x=f(p) for which dxdp=6000p(p216)32 that satisfies the initial condition x=5000 when p=$5.

Explanation

Given Information:

The provided equation of derivative of the demand function is dxdp=6000p(p216)32 and the initial

condition is x=5000, when p=\$3.

Formula Used:

According to the general power rule for integration,

If u is a differentiable function of x, then

undu=un+1n+1+C

where n1

Calculation:

Consider the equation dxdp=6000p(p216)32.

Integrate dxdp to obtain x.

x=6000p(p216)32dp

x=30002p(p216)32dp …… (1)

Let p216=u.

Differentiate with respect to p,

ddp(p216)=dudpddp(p2)ddp(16)=dudp2p=dudp2pdp=du

Substitute the value of 2pdp=du and p216=u in equation (1),

x=3000duu<

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