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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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  =  p p 2     25 x  = 600 when  p   =   $ 13

To determine

To calculate: The supply function x=f(p) for which dxdp=pp225 that satisfies the initial

condition x=600 when p=$13.

Explanation

Given Information:

The provided equation of derivative of the supply function is dxdp=pp225 and the initial

condition is x=600, when p=13.

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=pp225.

Integrate dxdp to obtain x.

x=pp225dp …… (1)

Let p225=u.

Differentiate with respect to p,

ddp(p225)=dudpddp(p2)ddp(25)=dudp2p=dudppdp=12du

Substitute the value of pdp=12du and p225=u in equation (1),

x=12udu

Now, apply the general power rule for integrtion in the above equation

x=12(u12+112+1)+C=12u32

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