It is known, from pre-calculus algebra, that a quadratic equation of the form

has a minimum point with x-coordinate

and y-coordinate

In this problem, x = t and f = W, and W(t) is a quadratic function with a = 0.03 > 0, b = -0.39, and c = 7.3.
So, the minimum weight occurs at

and the minimum weight is

This, of course, is the result we obtained using the other methods.

Derivative-free Introduction to Exercises