Question

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

Answer 1

hey, how's it going?

Answer 2

Awesome, you?

Answer 3

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

Answer 4

do you know what function we need the maximum of?

Answer 5

x-x^2?

Answer 6

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

Answer 7

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

Answer 8

err sorry you're right my bad

Answer 9

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

Answer 10

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

Answer 11

right

Answer 12

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

Answer 13

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

Answer 14

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