Derivatives Topics

Derivative as a Limit of Slopes

The derivative of the function f at x = a is the slope of...

Derivatives as an Instantaneous Rate of Change

Here we'll approach the derivative from a different and more real-lifey direction.There are two...

Tangent Lines

Daisy, our favorite track star, is learning how to throw discus via Youtube videos. She...

Tangent Line Approximation

There are only two things we need to remember about the tangent line to f at a. The tangent line...

Differentiability and Continuity

We've had all sorts of practice with continuous functions and derivatives. Now it's time to see...

The Derivative Function

The "derivative of f at a," written f ' (a), is a number that is equal to the slope of the...

Graphs of f ( x ) and f ' ( x )

From a graph of a function f(x) we can sketch graph of its derivative f ' (x). To do this,...

Theorems

Rolle's Theorem says:Let f be a function that is continuous on the closed interval...

In the Real World

Derivatives are, believe it or not, used a lot. The field of differential equations is an area of...