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Mathematics 30 Online
OpenStudy (anonymous):

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

OpenStudy (anonymous):

hey, how's it going?

OpenStudy (anonymous):

Awesome, you?

OpenStudy (anonymous):

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

OpenStudy (anonymous):

do you know what function we need the maximum of?

OpenStudy (anonymous):

x-x^2?

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

err sorry you're right my bad

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

right

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

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