derivatives and slopes of curves

[tmd1979]

What is the relationship between the slope of a curve and the derivative. I know that the limit of the derivative function is equal to the slope of the curve at that point. What else am I missing?

Also, what is the mathematical defintion for integrability?

Thanks.

 

[mmm4444bot]

What is the relationship between the slope of a curve and the derivative. The value of the derivative at a point is the slope at that point.

Also, what is the mathematical defintion for integrability? The word "integrability" is a noun. It means the quality of being integrable (having an antiderivative).