Applications of Derivatives: Optimization
1. Identify the variable you want to optimize, for example, you want to maximize area, A.
2. Identify the independent variable. For example, what is area going to be a function of? length and height, x and y?
3. Now you need an equation for A(x). It may be obvious or you may need a sketch to come up with the equation. Follow the steps we went over for problem solving.
4. Take the derivative, dA/dx.
5. Set it equal to zero and solve for x.
6. Check to see if this is a minimum or maximum by taking the second derivative. You can also look at a plot of the equation for this.
7. If it’s A you are solving for, plug x back into your original equation.