00:01
All right, hello! in this question we're asked to find the inflection point of this function, f of x equals x cubed over 6 minus 0 .7x squared over 2.
00:07
So to find the inflection point, we're going to need to find where our second derivative is equal to 0.
00:13
So we're going to first have to find our first derivative.
00:15
If we do that, we're going to get 3 over 6 times x squared minus 1 .4 over 2 times x.
00:22
And then i'm going to go ahead and just say that's 0 .5x squared minus 0 .7x.
00:29
If i take that derivative of that, i'll get my second derivative.
00:32
That's going to be 1x minus 0 .7.
00:37
I want to set that equal to 0.
00:38
So x equals 0 .7 is going to be my candidate for my inflection point.
00:43
Our inflection point isn't just where our second derivative equals 0, but it's where it changes signs.
00:51
So we have to make sure that f double prime actually changes signs here...