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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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Finding an Equation of a Function In Exercises 47-50, find an equation of the function f that has the given derivative and whose graph passes through the given point.

f ( x )   =   x 1  -  x 2 ( 0 ,   7 3 )

To determine

To calculate: The equation of the function f that has given derivative f(x)=x1x2

And given point (0,73).

Explanation

Given Information:

The provided derivative is f(x)=x1x2 and the provided point is (0,73).

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 derivative f(x)=x1x2.

It can be written as,

df(x)dx=x1x2

Integrate df(x)dx to obtain f(x).

f(x)=x1x2dx …… (1)

Let 1x2=u.

Differentiate with respect to x,

ddx(1x2)=dudxddx(1)ddx(x2)=dudx2x=dudxxdx=du2

Substitute the value of xdx=du2 and 1x2=u in equation (1),

f(x)=u122du

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

f(x)=12(u<

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