4 Suppose that f'(x) = 2x for all x a) Find f(5) if f(0) = 0. b) Find f(5) if f(4) = 14. c) Find f(5) if f(-1)=4. a) When f(0) = 0, f(5)= (Simplify your answer.) b) When f(4)= 14, f(5) = (Simplify your answer.) c) When f(-1) = 4, f(5)= (Simplify your answer.) H
4 Suppose that f'(x) = 2x for all x a) Find f(5) if f(0) = 0. b) Find f(5) if f(4) = 14. c) Find f(5) if f(-1)=4. a) When f(0) = 0, f(5)= (Simplify your answer.) b) When f(4)= 14, f(5) = (Simplify your answer.) c) When f(-1) = 4, f(5)= (Simplify your answer.) H
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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Question
![**Problem Statement:**
Suppose that \( f'(x) = 2x \) for all \( x \).
a) Find \( f(5) \) if \( f(0) = 0 \)
b) Find \( f(5) \) if \( f(4) = 14 \)
c) Find \( f(5) \) if \( f(-1) = 4 \)
**Solution Steps:**
a) When \( f(0) = 0 \), \( f(5) = \) [______]
(Simplify your answer)
b) When \( f(4) = 14 \), \( f(5) = \) [______]
(Simplify your answer)
c) When \( f(-1) = 4 \), \( f(5) = \) [______]
(Simplify your answer)
**Notes:**
- To solve these problems, you need to integrate \( f'(x) = 2x \) to find the general function \( f(x) \), and then apply the given conditions to solve for the constant of integration in each case.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02c8dc93-8b6f-4993-a985-0ce320a356a6%2F468a4064-0516-4b44-855f-7c7dd6d4c36e%2Foclesz5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Suppose that \( f'(x) = 2x \) for all \( x \).
a) Find \( f(5) \) if \( f(0) = 0 \)
b) Find \( f(5) \) if \( f(4) = 14 \)
c) Find \( f(5) \) if \( f(-1) = 4 \)
**Solution Steps:**
a) When \( f(0) = 0 \), \( f(5) = \) [______]
(Simplify your answer)
b) When \( f(4) = 14 \), \( f(5) = \) [______]
(Simplify your answer)
c) When \( f(-1) = 4 \), \( f(5) = \) [______]
(Simplify your answer)
**Notes:**
- To solve these problems, you need to integrate \( f'(x) = 2x \) to find the general function \( f(x) \), and then apply the given conditions to solve for the constant of integration in each case.
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