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Solve the initial-value problem by giving a function f(x) that satisfies 1 th f'(x) = x² – 4x - 5 and f(1) 3 %3D () ) Compute the average value of the function 1 f(x) = %3D aterval [1,9].

Solve the initial-value problem by giving a function f(x) that satisfies 1 th f'(x) = x² – 4x - 5 and f(1) 3 %3D () ) Compute the average value of the function 1 f(x) = %3D aterval [1,9].

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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**Problem 1: Solve the Initial-Value Problem** Find a function \( f(x) \) that satisfies the following conditions: - The derivative of the function is given by \( f'(x) = x^2 - 4x - 5 \); - The value of the function at \( x = 1 \) is \( f(1) = \frac{1}{3} \). **Problem 2: Compute the Average Value of the Function** Calculate the average value of the function \( f(x) = \frac{1}{\sqrt{x}} \) over the interval \([1, 9]\).
Transcribed Image Text:**Problem 1: Solve the Initial-Value Problem** Find a function \( f(x) \) that satisfies the following conditions: - The derivative of the function is given by \( f'(x) = x^2 - 4x - 5 \); - The value of the function at \( x = 1 \) is \( f(1) = \frac{1}{3} \). **Problem 2: Compute the Average Value of the Function** Calculate the average value of the function \( f(x) = \frac{1}{\sqrt{x}} \) over the interval \([1, 9]\).
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