Derivativefree Method
Consider equation
(1)
(1)

i.e.
(5)

Now, let us
complete the squares on the right hand side of equation (5).
Then,
or
i.e.
(6)

If we look
at the right hand side of equation (6), the first term 0.03(t13/2)^{2}
is either zero or positive for any tvalue and the second term is positive (check
this) all the time. This means that W will have a minimum when the first term
is zero (Are you clear on this?).
i.e. W will have a minimum when
or when
The minimum weight is
This is exactly the same answer we got earlier, in equation (4), by using the derivative method!