Find the real number which exceeds its square by the greatest amount.

Question

anonymous · Answer

hey, how's it going?

anonymous · Answer

Awesome, you?

anonymous · Answer

not bad, so it's asking for the greatest amount, which is another way of asking for a maximum, so we know we want the derivative of some function

anonymous · Answer

do you know what function we need the maximum of?

anonymous · Answer

x-x^2?

anonymous · Answer

There wasn't one given, so I just guessed that this one would be it.

anonymous · Answer

well we could do x-x^2, but then we'd just need to look for the minimum

anonymous · Answer

err sorry you're right my bad

anonymous · Answer

so yeah, take the derivative of that and set equal to 0

anonymous · Answer

1-2x=0...1/2?

anonymous · Answer

right

anonymous · Answer

Great! Thank you so much for all of your help! :)

anonymous · Answer

you can check that it is a maximum since it is positive to the left and negative to the right of 1/2

anonymous · Answer

Oh my gosh, I didn't even notice that or think to graph it.