I got the first part right need help with the second part. Can't figure it out The problem statement is: "Suppose $ F(t) $ has the derivative $ f(t) $ shown below, and $ F(0) = 3 $. Find values for $ F(1) $ and $ F(8) $."### Graph Description:- The graph illustrates the function $ f(t) $, which is the derivative of $ F(t) $.- The horizontal axis (x-axis) is labeled with values ranging from 0 to 8.- The vertical axis (y-axis) is labeled with values ranging from -3 to 3.### Graph Analysis:- The graph has a red line that consists of several segments: - From $ t = 0 $ to $ t = 1 $, the line rises linearly from $-1$ to $3$. - From $ t = 1 $ to $ t = 2 $, the line descends linearly from $3$ to $-2$. - From $ t = 2 $ to $ t = 8 $, the line remains constant at $-3$.### Derivative Analysis:- The derivative $ f(t) $ provides the rate of change of $ F(t) $.- The graph indicates: - Positive slope from $ t = 0 $ to $ t = 1$. - Negative slope from $ t = 1 $ to $ t = 2$. - Zero slope (constant value) from $ t = 2 $ to $ t = 8$.### Calculation:- To find $ F(1) $, integrate $ f(t) $ from 0 to 1 and add it to $ F(0) = 3 $.- To find $ F(8) $, integrate $ f(t) $ from 0 to 8 and add it to $ F(0) = 3 $.### Results:- $ F(1) $ is confirmed to be correct with the value $ 4 $.- The value for $ F(8) $ is left blank, to be determined by performing the integration and adding it to the initial value $ F(0) $.

To find F(8), use the properties of definite integral and calculate F0+∫08ftdt.…

Answered: Suppose F(t) has the derivative f (t)…

Suppose F(t) has the derivative f (t) shown below, and F(0) = 3. Find values for F(1) and F(8) 3+ -1 3 4 5 8 -1 -2 -3- F(1) : 4 F(8) =

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

I got the first part right need help with the second part. Can't figure it out

The problem statement is: "Suppose $ F(t) $ has the derivative $ f(t) $ shown below, and $ F(0) = 3 $. Find values for $ F(1) $ and $ F(8) $."

### Graph Description:
- The graph illustrates the function $ f(t) $, which is the derivative of $ F(t) $.
- The horizontal axis (x-axis) is labeled with values ranging from 0 to 8.
- The vertical axis (y-axis) is labeled with values ranging from -3 to 3.

### Graph Analysis:
- The graph has a red line that consists of several segments:
- From $ t = 0 $ to $ t = 1 $, the line rises linearly from $-1$ to $3$.
- From $ t = 1 $ to $ t = 2 $, the line descends linearly from $3$ to $-2$.
- From $ t = 2 $ to $ t = 8 $, the line remains constant at $-3$.

### Derivative Analysis:
- The derivative $ f(t) $ provides the rate of change of $ F(t) $.
- The graph indicates:
- Positive slope from $ t = 0 $ to $ t = 1$.
- Negative slope from $ t = 1 $ to $ t = 2$.
- Zero slope (constant value) from $ t = 2 $ to $ t = 8$.

### Calculation:
- To find $ F(1) $, integrate $ f(t) $ from 0 to 1 and add it to $ F(0) = 3 $.
- To find $ F(8) $, integrate $ f(t) $ from 0 to 8 and add it to $ F(0) = 3 $.

### Results:
- $ F(1) $ is confirmed to be correct with the value $ 4 $.
- The value for $ F(8) $ is left blank, to be determined by performing the integration and adding it to the initial value $ F(0) $.

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