00:01
So in order to find the critical points of this function, we're going to have to find this function's derivative f prime of x.
00:08
And so that's going to be equal to the derivative of e to the negative x plus two times the derivative of x of x.
00:17
And so all i did was since we have two terms here, the derivative of those terms together or added together is equal to the derivative of the first term plus the second term.
00:26
And then i just took the constant out of the second term.
00:29
And so to find the derivative of e to the negative x, we're going to treat it as if it were just e to the x.
00:34
And so the derivative of e to the x is itself.
00:37
However, instead of x here, we have negative x.
00:39
And then all we need to do is multiplied by the derivative of negative x.
00:43
And the derivative of negative x is negative 1.
00:46
And so we have negative e to the negative x power.
00:48
And then plus two times the derivative of x.
00:51
And this is a power rule derivative, and the derivative of x is just equal to 1.
00:55
So we're going to have our derivative function as negative.
00:58
E to the negative x power plus two...