Final answer:
The question appears to involve the First Order Necessary Conditions (FONC) in calculus, which state that for an extremum of a function f(x), the derivative f' (x*) must be zero. The provided condition, 1 − ax* = 0, can be derived from setting the derivative of the function f(x) = 1 − ax to zero, which satisfies FONC.
Step-by-step explanation:
The question seems to be related to the First Order Necessary Conditions (FONC) for an optimization problem in calculus.
Given a function f(x), the FONC states that if x* is a local extremum (maximum or minimum) of f(x), then f' (x*) = 0, provided that f is differentiable at x*.
In mathematical terms, if 'a' represents a constant and 'x*' represents the value of x at the extremum, the condition provided translates as 1 − ax* = 0.
To show this, we assume that the function f(x) in question is f(x) = 1 − ax; its derivative f'(x) would be −a. Setting the derivative equal to zero yields −a = 0 or x* = 1/a as the point where the function might achieve an extremum.
This aligns with the FONC which requires the derivative at an extremum to be zero.
In context, it's possible that there has been a misunderstanding or typo in the original question.
Without full context, it's challenging to provide a complete answer, but the above explanation should clarify how the FONC works for an extremum of a function.