That looks right. x = 0 is a critical number too though because it causes f(c) to no longer exist, but that's outside the interval. Did you test the end points? There's a theorem (I think extreme value theorem) that says there should be an absolute maximum and minumum in that interval which means there'll be another critical number in that interval.
not true ... x = c is a critical value of f(x) if f(c) is defined and f'(c) = 0 or f'(c) is undefined. Endpoint extrema are not necessarily critical values. Recommend you check out the link re: definition of a critical value.
Pauls Online Notes : Calculus I - Critical Points