# How do you find the local extremas for #x(x-1)# on [0,1]?

##### 1 Answer

Dec 9, 2016

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

**minimum** at