Take the first derivative of the equation that models the nonlinear pricing. These pricing models often follow simple polynomial patterns. Their derivatives are often easily taken using the "power rule" of derivatives. For example, a parabolic price function of f (x) = (x^2) +15, has a first derivative equal to f ' (x) = 2x. This new equation is spoken "F prime of x."
Set the resulting derivative equation equal to zero. Following the example: f ' (x) = 2x = 0.
Solve the derivative function for the variable that represents price. This variable is most commonly represented as "x" in the equation. It is at this point in the graph of the original function that the optimal price is found. Prior to this point, assuming parabolic growth, the savings is not at its maximum. Also, past this point, the savings in price begins to diminish. For example, the result of solving the derivative equation is 0. Therefore, substitute 0 into the original function, f (0) -> (x^2) +15 = (0^2) +15 = 15. The solution to this pricing equation is found at x = 0 and has a value of 15.