Application of Derivatives Overview

Remember that the derivatives you find are a tool for telling you information about something else. They are not the end of a process, but the beginning of a process. If we go back to the Algebra vs. Calculus idea, what you have found by “finding the derivative” is just the equation for finding the slope at a point. In algebra you have found $\frac{{\mathit{y}}_{\mathit{2}}\mathit{–}{\mathit{y}}_{\mathit{1}}}{{\mathit{x}}_{\mathit{2}}\mathit{–}{\mathit{x}}_{\mathit{1}}}$, and in calculus you have found $f^{\prime }\left(x\right)$. All you have is an equation. From there you have to put the equation to use

What you will see here are several different ways that you can apply your derivative tool. You will see that a common Step 1 throughout all the methods in this section will be to “Find the derivative”. Please make sure your derivative skills are solid before you move forward.