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Suppose f"(x) = 42x 2, f'(2) = 78, and f(2) = 57. Then f(x) = Question Help: D Video B Written Example Message instructor Submit Question

Suppose f"(x) = 42x 2, f'(2) = 78, and f(2) = 57. Then f(x) = Question Help: D Video B Written Example Message instructor Submit Question

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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Suppose \( f''(x) = 42x - 2 \), \( f'(2) = 78 \), and \( f(2) = 57 \). Then \( f(x) = \) [ ] **Question Help:** - Video - Written Example - Message instructor [Submit Question]
Transcribed Image Text:Suppose \( f''(x) = 42x - 2 \), \( f'(2) = 78 \), and \( f(2) = 57 \). Then \( f(x) = \) [ ] **Question Help:** - Video - Written Example - Message instructor [Submit Question]
**Problem Statement:** Consider the function \( f(x) \) whose second derivative is \( f''(x) = 9x + 6\sin(x) \). If \( f(0) = 3 \) and \( f'(0) = 4 \), what is \( f(3) \)? **Instructions:** You are provided with the second derivative of the function \( f(x) \). Using the initial conditions \( f(0) = 3 \) and \( f'(0) = 4 \), find the value of \( f(3) \). **Features:** - **Submit Question Button:** Click this button to submit your answer once you have found \( f(3) \). - **Message Instructor Option:** Use this feature if you need assistance or have questions regarding the problem. **Note:** Make sure to integrate the second derivative step-by-step to find the first and then the original function, applying the initial conditions to solve for constants of integration.
Transcribed Image Text:**Problem Statement:** Consider the function \( f(x) \) whose second derivative is \( f''(x) = 9x + 6\sin(x) \). If \( f(0) = 3 \) and \( f'(0) = 4 \), what is \( f(3) \)? **Instructions:** You are provided with the second derivative of the function \( f(x) \). Using the initial conditions \( f(0) = 3 \) and \( f'(0) = 4 \), find the value of \( f(3) \). **Features:** - **Submit Question Button:** Click this button to submit your answer once you have found \( f(3) \). - **Message Instructor Option:** Use this feature if you need assistance or have questions regarding the problem. **Note:** Make sure to integrate the second derivative step-by-step to find the first and then the original function, applying the initial conditions to solve for constants of integration.
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