The derivative of a function is another function, which measures the instantaneous rate of change of the original function.

The derivative is a magical tool that encodes relative movement information into arithmetic information. It gives us a way to “calculate” increasing and decreasing.

Calculus will provide a procedure for deriving the derivative of any function. With the derivative, we will be able to, algebraically, calculate where a function is increasing and decreasing. This will give us methods for tracking down local maximums and minimums. Optimization a most popular goal in science.

Currently we know how to get formulas for the derivatives of a linear function and a quadratic function. That’s it!

This isn’t much, but it gives us enough experience to prepare for Calculus.

In this course, we will add the derivatives of sine and cosine, which will give us a bit more experience heading to Calculus.

Calculus will give us a procedure to obtain formulas for derivatives ourselves. In this course, we can just be supplied the derivative and use it to help our analysis of functions right now.

Thst’s what we’ll do in this section.

Learning Outcomes

In this section, students will

• analyze functions using the derivative.