00:01
This problem wants us to find the absolute maximum value and the absolute minimum value, if any, of the function.
00:06
And we're given the function f of x equals x squared minus x minus 6 on the interval 0 to 6, where 0 and 6 are both included.
00:13
And since we're looking for absolute maximums and absolute minimums, we can just compare the outputs at the locations of these possible extrema.
00:20
And to find those locations, we can find our first derivative of our function.
00:24
By first taking our 2 and multiplying by the coefficient of understood 1 to give us 2x raised to the 2 minus 1, or just to the first power.
00:31
The derivative of a linear term is just the coefficient, which would be negative 1 here.
00:35
And the derivative of any constant is just 0, so our negative 6 is gone.
00:39
And now we'll set our first derivative equal to 0 to solve for the locations of potential extrema.
00:45
And when we add 1 over, we get 2x equal to 1.
00:47
And when we divide by 2, that gives us x equals 1 half, which is on our interval...