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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5, Problem 17RE
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding a Particular Solution In Exercises 15–18, find the particular solution that satisfies the differential equation and the initial condition.

f ' ( x ) = x ;     f ( 9 ) = 4

To determine

To calculate: The particular solution that satisfied the differential equation and initial condition f′(x)=x and  f(9)=4.

Explanation

Given Information:

The provided differential equation f′(x)=x.

The initial condition f(9)=4

Formula used:

The power rule of integrals:

∫undu=un+1n+1+C (for n≠1)

Here, u is function of x.

The property of Intro-differential:

∫df(x)dxdx=f(x)

Calculation:

Consider the derivative equation:

f′(x)=x

Rewrite the integrand as:

df(x)dx=x

Apply, integration on both sides:

∫df(x)dxdx=∫(x)dx+C

Now apply the power rule of integration and property of Intro-differential:

<

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Applying the First Derivative Test In Exercises 27-34, (a) find the critical numbers of f, if any, (b) find the...

Calculus (MindTap Course List)

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