00:01
What i would do in this problem is take the derivative.
00:05
And we have a quotient happening, so you better do the quotient rule.
00:11
And so what's the quotient rule is you take the derivative of the top, you leave the bottom alone, and you subtract off the derivative of the bottom, leaving the top alone, all over the denominator squared.
00:25
And so where your max and minimal curve is if the numerator is equal to zero.
00:34
Now the denominator cannot equal zero just because you're square.
00:39
You'll get a positive plus three is a positive, so it's impossible.
00:43
So if i distribute in the numerator where we have 6x squared plus 18 minus 12x squared is equal to 0.
00:52
So combining like terms, you give me negative 6x squared.
00:55
I'll go ahead and subtract 18 to the right side.
01:06
And if you divide that negative 6 over, we get x squared equals 3.
01:12
And so your min and max will happen at positive or negative root 3.
01:17
So since i'm not seeing any, i'm going to choose the option that says none of these.
01:25
And i feel pretty good about that because, well, i'm looking at a graphic calculator.
01:31
If you were to plug in root 3 in for these x's, you end up with 6 root 3 over root 3 squared as positive 3 plus 3 is 6.
01:43
So we have a max at root 3, root 3, because those 6es will cancel...