00:01
We are trying to find the absolute extrema for this function on the given interval.
00:05
First, let's determine the critical numbers.
00:09
The derivative of our function, if we bring the two -thirds out front, that would give us six -thirds or two, and then we will subtract one from the power.
00:19
So this is two over the cube root of theta.
00:26
Critical numbers would occur either where h -prime is zero, or where the function is non -differentiore.
00:32
Well, h prime is never going to be zero because fractions are zero if the top is zero, but we have a top value of two.
00:42
It is, though, non -differential when the denominator is zero, and that is very obviously zero when theta is zero.
00:54
So let's take a look at the values of the function at the end points and at the critical point.
01:06
If we fill in negative 27 for theta into the original function.
01:12
The cube root of negative 27 is negative 3...