Tangent of a graph

  • #1
disregardthat
Science Advisor
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Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
mathman
Science Advisor
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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
disregardthat
Science Advisor
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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
1,425
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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
disregardthat
Science Advisor
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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!
 

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