00:01
So in order to find the critical points of the function, we need to find the function's derivative, set it equal to zero, and solve for x.
00:07
So the first thing i'm going to do is actually split this up into two fractions.
00:11
So we're going to have one divided by x to the one -half power, which is the same thing as x to the negative one -half power, and then plus x divided by x the one -half power, which we can just minus the exponent in the denominator from that in the numerator.
00:24
And so we're going to get x to the negative one half power plus x to the one half power.
00:30
And so our derivative function is going to be pretty straightforward to find.
00:34
It's just going to be two power rules.
00:35
So we're going to bring down the negative one half.
00:38
And we're going to minus one to the power.
00:39
So now we're going to have negative three halves and negative x divided by two.
00:44
We're going to do the same thing here...