To find the global extrema, check the local extrema and the limit of the function approaching the bounds.

Local extrema:

We have a local extremum at . What's f(x) of the point?

Now check the bounds.

We have 3 possible values to be the global extrema.

-- (the local extrema, x=1)

-- (left bound)

-- (right bound)

The greatest of these values, is the global maximum, and the least, is the global minimum.