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Find a function that satisfies the conditions f " (x)=x8, f'(0) = 13, f(0) = 10.

Find a function that satisfies the conditions f " (x)=x8, f'(0) = 13, f(0) = 10.

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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**Title: Finding a Function that Satisfies Given Conditions** **Problem Statement:** Find a function \( f(x) \) that satisfies the following conditions: - The second derivative \( f''(x) = x^8 \). - The first derivative at zero \( f'(0) = 13 \). - The function value at zero \( f(0) = 10 \). **Options:** a) \( f(x) = \frac{1}{10}x^{10} + 13x \) b) \( f(x) = \frac{1}{90}x^9 + 13x + 10 \) c) \( f(x) = \frac{1}{90}x^9 + 10x + 13 \) d) \( f(x) = \frac{1}{9}x^9 + 13x \) e) \( f(x) = \frac{1}{90}x^{10} + 13x + 10 \) Select the correct function from the options above that satisfies all given conditions.
Transcribed Image Text:**Title: Finding a Function that Satisfies Given Conditions** **Problem Statement:** Find a function \( f(x) \) that satisfies the following conditions: - The second derivative \( f''(x) = x^8 \). - The first derivative at zero \( f'(0) = 13 \). - The function value at zero \( f(0) = 10 \). **Options:** a) \( f(x) = \frac{1}{10}x^{10} + 13x \) b) \( f(x) = \frac{1}{90}x^9 + 13x + 10 \) c) \( f(x) = \frac{1}{90}x^9 + 10x + 13 \) d) \( f(x) = \frac{1}{9}x^9 + 13x \) e) \( f(x) = \frac{1}{90}x^{10} + 13x + 10 \) Select the correct function from the options above that satisfies all given conditions.
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