How do you find the local extremas for #x(x-1)# on [0,1]?
Finding local extremas involves the first derivative being set equal to 0; then finding out how the derivative acts as you plug in values greater or less than those zeros.
Therefore, we can rewrite
This lies on the interval
So, a local extrema is possible, not guaranteed.
However, since the multiplicity of our function is odd, that is:
There will be a local extrema at
Let's plug in
Again, since the multiplicity is odd, there will be a positive slope from