The picture is the problem*Please use handwriting not typing, I understand it better that way, thank you* **Problem 44:**Given the function \( F(x) = \int_2^x f(t) \, dt \), where \( f \) is the function shown in the graph, determine which of the following values is largest:- (A) \( F(0) \)- (B) \( F(1) \)- (C) \( F(2) \)- (D) \( F(3) \)- (E) \( F(4) \)**Graph Explanation:**The graph provided displays the function \( y = f(t) \), with the x-axis representing \( t \) and the y-axis representing \( y \). The graph shows the following characteristics:- The function \( f(t) \) starts above the x-axis at \( t = 0 \), achieving a peak before descending through the x-axis.- It becomes negative just after \( t = 1 \) and remains below the x-axis until \( t = 4 \).- At \( t = 2 \), the graph crosses the x-axis again and continues to decrease, reaching a minimum between \( t = 3 \) and \( t = 4 \).- The graph starts rising after \( t = 4 \).For \( F(x) \), the value is determined by the area under the curve of \( f(t) \) from 2 to \( x \). Positive areas above the x-axis contribute positively to \( F(x) \), while areas below subtract from the total.To solve the problem, consider the net area accumulated for each interval and identify when the positive versus negative areas result in the greatest accumulated value for \( F(x) \).

Answered: Image /qna-images/answer/bf19ed42-7a6d-402b-91ec-057cffb6d553.jpg

Answered: If F(x) = f(t) dt, where fis the…

If F(x) = f(t) dt, where fis the function whose graph is given, which of the following values is largest? (B) F(1) (D) F(3) (A) F(0) (C) F(2) (E) F(4) ya 120 15 (10

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

The picture is the problem *Please use handwriting not typing, I understand it better that way, thank you*

**Problem 44:**

Given the function \( F(x) = \int_2^x f(t) \, dt \), where \( f \) is the function shown in the graph, determine which of the following values is largest:

- (A) \( F(0) \)
- (B) \( F(1) \)
- (C) \( F(2) \)
- (D) \( F(3) \)
- (E) \( F(4) \)

**Graph Explanation:**

The graph provided displays the function \( y = f(t) \), with the x-axis representing \( t \) and the y-axis representing \( y \). The graph shows the following characteristics:

- The function \( f(t) \) starts above the x-axis at \( t = 0 \), achieving a peak before descending through the x-axis.
- It becomes negative just after \( t = 1 \) and remains below the x-axis until \( t = 4 \).
- At \( t = 2 \), the graph crosses the x-axis again and continues to decrease, reaching a minimum between \( t = 3 \) and \( t = 4 \).
- The graph starts rising after \( t = 4 \).

For \( F(x) \), the value is determined by the area under the curve of \( f(t) \) from 2 to \( x \). Positive areas above the x-axis contribute positively to \( F(x) \), while areas below subtract from the total.

To solve the problem, consider the net area accumulated for each interval and identify when the positive versus negative areas result in the greatest accumulated value for \( F(x) \).

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