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Find an equation for the function f that has the given derivative and whose graph passes through the given point. f'(x) = -2x√8-x² (2,7) f(x) = Derivative Point

Find an equation for the function f that has the given derivative and whose graph passes through the given point. f'(x) = -2x√8-x² (2,7) f(x) = Derivative Point

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** Find an equation for the function \( f \) that has the given derivative and whose graph passes through the given point. **Given:** - **Derivative:** \( f'(x) = -2x \sqrt{8 - x^2} \) - **Point:** \( (2, 7) \) **Solution:** Determine the function \( f(x) \). **Assistance Available:** If you need help, click the "Read It" button to access additional resources. --- In this problem, you are tasked with finding the original function \( f(x) \) given its derivative \( f'(x) = -2x \sqrt{8 - x^2} \) and a point \( (2, 7) \) that lies on the graph of the function. The derivative provided suggests the use of integration to find the original function, and the given point will be essential for determining the constant of integration.
Transcribed Image Text:**Problem Statement:** Find an equation for the function \( f \) that has the given derivative and whose graph passes through the given point. **Given:** - **Derivative:** \( f'(x) = -2x \sqrt{8 - x^2} \) - **Point:** \( (2, 7) \) **Solution:** Determine the function \( f(x) \). **Assistance Available:** If you need help, click the "Read It" button to access additional resources. --- In this problem, you are tasked with finding the original function \( f(x) \) given its derivative \( f'(x) = -2x \sqrt{8 - x^2} \) and a point \( (2, 7) \) that lies on the graph of the function. The derivative provided suggests the use of integration to find the original function, and the given point will be essential for determining the constant of integration.
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