Use profit-maximization and revealed choices by firms to show the law of supply

Use profit-maximization and revealed choices by firms to show the law of supply. Be sure to define what is meant by “the law of supply”?
Hint:
p1 q1 - w x1 >= p1 q2 - w x2
revealed profits question
theoretical version prove results when you don't know the production function assume production functions are differentiable and continuous these are results that are true even when the production function is not differentiable about profit max
q1` x1 and q2 x2 are both feasible
if p1 >= p2
you know nothing else about p1 and p2
then x1 >= x2
no govt involved
w
input demand curve

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