The slope of a curve at a point is defined to be the slope of the tangent line. Thus the slope of a curve is found using the derivative.
Everyone knows slope is the change of y over the change of x
You use that to find the AVERAGE slope between two points. But some may ask how to find the slope at a GIVEN POINT.
They may think it is impossible by combining what they have learned and common knowledge. But they are wrong.
With derivatives you shrink the point (two points) to the smallest possible distance... but then you eventually shrink it down to zero.
How to Find a Derivative!
You start off with the original slope formula like the one above, but with a little twist.
f(x+h)-f(x)= y
h=x
Once you simply that formula, that gives you the average slope of the graph. Then from that you plug in a point and voila! the slope at that given point.
Like I said earlier, eventually you turn "h" into 0
So the final average slope of the formula above is "2x"
For more help visit: http://www.coolmath.com/precalculus-review-calculus-intro/precalculus-algebra/24-the-difference-quotient-01.htm
Thank You,
Peter Kessel
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