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OpenStudy (anonymous):
Find the real number which exceeds its square by the greatest amount.
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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?
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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?
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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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