Max and Min of a Function

A minimum or maximum value of a function occurs where the derivative of the function is zero (i.e. on a graph of the function, the line will be horizontal).

We can derive a symbolic expression for the min/max or a function as follows:

1. Find the derivative of the rhs of the equation with respect to the independent variable.

2. Make a new equation, setting the derivative to zero.

3. Solve the new equation for the independent variable.

4. Simplify the rhs of the equation.

(def cannonball
     '(= y (- (* (* v (sin theta)) t)
              (* (/ g 2) (expt t 2)))) )