Calculate Rate of Growth for Tangent of a Graph

[disregardthat]

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?

 

[mathman]

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.

 

[disregardthat]

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?

 

[Werg22]

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.

 

[disregardthat]

Man!

 

[anantchowdhary]

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!