Calculate Rate of Growth for Tangent of a Graph

In summary, the conversation discusses finding the tangent of a point on a graph, specifically for the function f(x)=x^2. The concept of derivatives and how they relate to the slope of a tangent is also mentioned. The end result is finding the slope of the tangent at x=2, which is 4.
  • #1

disregardthat

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Is is possible to calculate the growth-rate to a tangent in a graph? (like f(x)=x^2

I only know how to draw the line on the graph, but how do you calculate it if you know the point where you must draw the tangent?

For example: find the tangent of the point x=2 on a graph f(x)=x^2

How do you find the rate of growth?
 
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  • #2
This is one of the first things you learn about in elementary calculus. The tangent (slope) at a point on a curve is given by the first derivative at that point.
 
  • #3
I have only had one class in calculus, and we learned the average rate of change. Then we got two points in a graph, and calculated the average slope. I know what a tangent of a graph is, and I have managed to sort out the somewhat accurate answer with only drawing the line, but I don't know how to calculate it.

And what is a derivative? Is a derivative the average slope for two points of the x-axis on a graph?
 
  • #4
Your are talking about the whole limiting process that the derivative is. You will eventually learn how to calculate the slope of the tangent with analytical methods if you follow a calculus course.
 
  • #5
Man!

:tongue2:
 
  • #6
The slope here for x=2 is 4.If you take the derivative of f(x)=x^2,you get dy/dx=2x

now substitute the value of x and you get the slope!
 

1. How do I calculate the rate of growth for a tangent of a graph?

To calculate the rate of growth for a tangent of a graph, you need to find the derivative of the function at the point where the tangent line intersects the graph. This derivative represents the slope of the tangent line and can be used to calculate the rate of growth.

2. Can I use any point on the graph to calculate the rate of growth for a tangent?

No, you need to select a specific point on the graph where the tangent line intersects. This point will be used to calculate the derivative and determine the rate of growth for the tangent.

3. Is there a specific formula for calculating the rate of growth for a tangent?

Yes, the formula for calculating the rate of growth for a tangent is the same as the formula for calculating the slope of a line: (y2 - y1) / (x2 - x1). However, you need to use the coordinates of the point where the tangent line intersects the graph as your (x1, y1) values.

4. What does the rate of growth for a tangent represent?

The rate of growth for a tangent represents the instantaneous rate of change of the function at a specific point. In other words, it tells you how quickly the function is changing at that point.

5. Can I use the rate of growth for a tangent to predict future values of the function?

Yes, you can use the rate of growth for a tangent to make predictions about the future behavior of the function at that point. This is because the rate of growth gives you information about the rate of change, which can be used to extrapolate the function's values.

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