Derivative applications

Equations of normal and tangent lines

A derivative at a point in a curve can be viewed as the slope of the line tangent to that curve at that point. Given this, the natural next question is what the equation of that tangent line is. In this tutorial, we'll not only find equations of tangent lines, but normal ones as well.

Critical points and graphing with calculus

One of the reasons calculus was invented was to be able to optimize functions. When you have some function modeling a real world situation, you often want to find its maximum or minimum. In this tutorial, you will see how information about the derivative of a function can give powerful ways to mathematically describe the "shape" of a function.

Absolute and relative maxima and minima

When you're looking for the maximum or minimum of a function, a good way to start is by finding points where the derivative equals zero. However, you won't always get the maximum possible value of the function; you might just end up with a point which is maximum *relative* to those points around it. In this tutorial, you will learn about the extreme value theorem, and what it tells us about relative maxima and minima.

Tangents to polar curves

Here you have the chance to practice thinking about tangent lines when curves are defined in polar coordinates.