00:01
Alright, so given our function as x minus 8 times e to the negative x, we can rewrite this as x minus 8 over e to the 9x.
00:13
So finding our derivative function, that's going to be e to the 9x squared.
00:22
The derivative of the numerator is just 1, so it's just e to the 9x.
00:29
And then minus x minus 8, and then times 9e to the 9x.
00:39
Setting that equal to zero.
00:42
So our denominator, we cancel out when we multiply both sides.
00:46
So e to the 9x minus 9 times x minus 8 e to the 9x.
00:56
So let's pull out an e to the 9x.
00:59
So 1 minus 9 times x minus 8, so that's going to be 9x, and then plus 72.
01:09
So e to the 9x set equal to zero, and then this is 73 minus 9x set equal to zero.
01:23
So introducing natural log, well we actually don't, we can't take the natural log of this, so we ignore that side.
01:31
Solving for x over here, 73 equal to, i believe 73 is not divisible by 9, so 73 over 9 for our x.
01:45
So plot that on a number line, 73 over 9...