00:01
We are looking for the critical numbers for this function, and i am going to rewrite the function to be 2x minus x squared to the one -half power.
00:13
The derivative of that function, using the chain rule, would be one -half times 2x minus x squared to the negative one -half power, times the derivative of the inside of the quantity, which would be two, minus 2x.
00:34
If i distribute the 1 half into the 2 minus 2x, the 2s are all going to cancel.
00:40
So now rewritten, i have 1 minus x over the square root of 2x minus x squared.
00:51
Now, this would be non -differentialable any time the bottom is equal to 0, which if i factor out the 2, what do i get? times 2 minus x, so that would be true if x is 0 or 2.
01:13
So those are two critical points.
01:16
Other critical points could be when the derivative is equal to 0...