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Solve the initial value problem: find the function f(x) if f"(x) = x5/2 and f'(16) = 3 and r(0) = 0.

Solve the initial value problem: find the function f(x) if f"(x) = x5/2 and f'(16) = 3 and r(0) = 0.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Initial Value Problem** Solve the initial value problem: Find the function \( f(x) \) if \( f''(x) = x^{-5/2} \) and \( f'(16) = 3 \) and \( f(0) = 0 \). **Explanation:** This problem involves finding a function \( f(x) \) that satisfies the given conditions. The process includes: 1. **Integration**: Integrate \( f''(x) = x^{-5/2} \) to find \( f'(x) \). 2. **Use given condition**: Apply \( f'(16) = 3 \) to determine the constant of integration. 3. **Integrate again**: Integrate the result to find \( f(x) \). 4. **Apply initial condition**: Use \( f(0) = 0 \) to find the final constant of integration. These steps will lead you to the function \( f(x) \).
Transcribed Image Text:**Initial Value Problem** Solve the initial value problem: Find the function \( f(x) \) if \( f''(x) = x^{-5/2} \) and \( f'(16) = 3 \) and \( f(0) = 0 \). **Explanation:** This problem involves finding a function \( f(x) \) that satisfies the given conditions. The process includes: 1. **Integration**: Integrate \( f''(x) = x^{-5/2} \) to find \( f'(x) \). 2. **Use given condition**: Apply \( f'(16) = 3 \) to determine the constant of integration. 3. **Integrate again**: Integrate the result to find \( f(x) \). 4. **Apply initial condition**: Use \( f(0) = 0 \) to find the final constant of integration. These steps will lead you to the function \( f(x) \).
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