Understanding the Relationship between Functions and Graphs

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Homework Help Overview

The discussion revolves around finding the area between the graphs of the linear function f(x) = 2x + 1 and the quadratic function g(x) = x^2 + 1, specifically over the interval from x = 0 to x = 2. Participants are exploring how to determine which graph is upper in this region and discussing the process of integration related to this problem.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss calculating points of intersection and the need to identify the upper graph. Some suggest sketching the graphs to visualize the functions. Others raise questions about the rules of antiderivatives and their relationship to derivatives, particularly in the context of integration.

Discussion Status

The discussion is active, with participants sharing their attempts and questions regarding the problem. There is a focus on understanding the relationship between functions and their integrals, as well as clarifying the concept of upper and lower graphs in the context of area calculation.

Contextual Notes

Some participants express uncertainty about the rules for antiderivatives and their application, indicating a need for further clarification on these concepts. There is a mention of resources for learning, but no specific solutions or methods have been provided.

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Homework Statement



Problem: Find the area of the region that is bounded by the graphs of f(x) = 2x+1, and g(x) = x^2 +1

I have calculated the points of intersection, but am having trouble figuring out which is the upper graph over this interval:

x=0 & x=2

Are there any resources you can point me to so as I can learn to distinguish?

Many thanks in advance.
 
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sdoman said:

Homework Statement



Problem: Find the area of the region that is bounded by the graphs of f(x) = 2x+1, and g(x) = x^2 +1

I have calculated the points of intersection, but am having trouble figuring out which is the upper graph over this interval:

x=0 & x=2

Are there any resources you can point me to so as I can learn to distinguish?
  • Brain
  • Hand
  • Paper
  • Pencil
Sketch a graph of the two functions. One graph is a straight line; the other is a parabola.

sdoman said:
Many thanks in advance.
 
Ha sounds good man.

Another question:

I have the anti derivative from 0 to 2 (2x-x^2) dx

and then the example states we get (x^2 - (x^3)/3) over the same interval.

My question is about the 2x after we integrate it we get x^2.

So if we have 4x would it be x^2 or x^4?

Thanks
 
Do you know any rules for antiderivatives? Do you know how derivatives and antiderivatives are related?
 
I am having trouble with them.
 
I do know the basics in how they are related I guess you could say
 
What rules do you know?

sdoman said:
I do know the basics in how they are related I guess you could say
OK, how are they related?
 

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