calculate the number whose difference between itself and its square is a maximum

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calculate the number whose difference between itself and its square is a maximum

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Incomplete info. as it is x-x^2=max
how is the info incomplete?
a maximum: a maximum means nothing in of itself, a maximum to what?!

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the maximum difference between any two real numbers
sorry the maximmum difference between any number and its square
for example for 0.8 the difference is .8 - .8^2 = .16
Ok, so we want to maximize \(f(x)=x-x^2\) Without calculus: find the vertex \(x=-b/2a=-1/(2(-1))=1/2\). So it is maximum when \(x=1/2). With calculus, set \(f'(x)=1-2x=0\). Hence \(x=1/2\). Then you just need to justify that x=1/2 gives the maximum value.
this is how i interpreted the question
right! how the heck didn't i think of that - ty. how do i give medals?
Press the good answer button :)

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