A zero derivative hides a finite range

A bounded coordinate x can lie anywhere in the interval from −3.0 mm to +2.0 mm. A derived quantity is y = x², and x = 0 is used as the nominal input. No probability distribution is specified.

What is the largest possible value of y?

Organize the givens & assumptions

Input interval: −3.0 mm ≤ x ≤ +2.0 mm
Derived quantity: y = x²

The bounds are hard input limits for this mathematical model. They are not standard deviations. Evaluate the entire interval, including its stationary point.

A $4.0\ \mathrm{mm^2}$
B $0$
C $9.0\ \mathrm{mm^2}$
D $25\ \mathrm{mm^2}$

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