Understanding the Graph of an Equation | Calculus Help

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In summary, the equation y = (2x^2)/(9-x2) tells you the value of y when x = 0, x = -3, and x = 3. The function is undefined at x = -3 and x = 3, but it has a vertical asymptote at x = 0.
  • #1
Bandarigoda
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Hi everyone, I'm learning calculus at school. Recently I was taught this equation like. Y = (2X^2)/(9 - X^2)
So the teacher did all by himself. So I came home and now confused. I know there are 3 graphs(sorry if the word is not right ) so I was doing it again. And I'm stuck at where to get the position of curves.

I got,
X = 0 , X = -3, X= 3
They are 3 graph. So I couldn't figure out how to get more positions and draw it. Unfortunately I can't remember what teacher did 100% .
So someone please demonstrate it for me from the steps I have done.

Thanks
 
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  • #2
I derived the functions and got their maximum /minimum
 
  • #3
Here
uploadfromtaptalk1371171154059.jpg
 
  • #4
Bandarigoda said:
Hi everyone, I'm learning calculus at school. Recently I was taught this equation like. Y = (2X^2)/(9 - X^2)
So the teacher did all by himself. So I came home and now confused. I know there are 3 graphs(sorry if the word is not right ) so I was doing it again. And I'm stuck at where to get the position of curves.

I got,
X = 0 , X = -3, X= 3
They are 3 graph. So I couldn't figure out how to get more positions and draw it. Unfortunately I can't remember what teacher did 100% .
So someone please demonstrate it for me from the steps I have done.

Thanks

Your work for the derivative is correct: dy/dx = 36x/(9 - x2)2

Bandarigoda said:
I derived the functions and got their maximum /minimum
No, you differentiated the function and found the values for which f' = 0 or where the derivative is not defined.

If you set dy/dx = 0, the only solution is x = 0. The tangent line is horizontal when x = 0 (at the point (0, 0)).

dy/dx is undefined where the denominator is zero; namely, when x = 3 or x = -3. The original function is also undefined at the numbers. These turn out to be vertical asymptotes. The graph of the function tends to +∞ or -∞ on either side of these asymptotes.

Since there are two of them, they divide the number line into three intervals: (-∞, -3), (-3, 3), and (3, ∞). These intervals correspond to the three graphs you're talking about.
 
  • #5
Hi, thank you very much Sir!
 

1. What is the purpose of understanding the graph of an equation in calculus?

Understanding the graph of an equation in calculus allows us to visualize and analyze the behavior of a mathematical function. It helps us to understand the relationship between different variables and how they change over a given domain.

2. How do I find the x and y-intercepts of a graph?

To find the x-intercept, set y = 0 and solve for x. To find the y-intercept, set x = 0 and solve for y. These points represent where the graph crosses the x and y-axes, respectively.

3. How do I determine the slope of a graph?

The slope of a graph can be found by calculating the change in y over the change in x, also known as rise over run. This can be done by choosing two points on the graph and using the formula (y2 - y1)/(x2 - x1).

4. What is the difference between a linear and non-linear graph?

A linear graph represents a straight line and its equation can be written as y = mx + b, where m is the slope and b is the y-intercept. A non-linear graph does not have a constant rate of change and its equation cannot be written in this form.

5. How does the shape of a graph relate to the behavior of a function?

The shape of a graph gives us information about the behavior of a function. For example, a positive slope indicates that the function is increasing, while a negative slope indicates that the function is decreasing. A steep slope indicates a faster rate of change, while a shallow slope indicates a slower rate of change. The curvature of a graph can also give us information about the concavity of a function.

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