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

Question

anonymous · Answer

Incomplete info. as it is x-x^2=max

anonymous · Answer

how is the info incomplete?

anonymous · Answer

a maximum: a maximum means nothing in of itself, a maximum to what?!

anonymous · Answer

the maximum difference between any two real numbers

anonymous · Answer

sorry the maximmum difference between any number and its square

anonymous · Answer

for example for 0.8 the difference is  .8 - .8^2 = .16

watchmath · Answer

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.

anonymous · Answer

this is how i interpreted the question

anonymous · Answer

right! how the heck didn't i think of that - ty. how do i give medals?

watchmath · Answer

Press the good answer button :)