Question

Find any absolute max/min and local max/min for the function f(x)=x^3-4x+5 on the interval [0,5). Made sure to prove that these points are max/min values.

This is what I did so far.

f'(x)=3x^2-4=0
3x^2=4
x= 2/sqrt3 The -2/sqrt3 is outside of interval so can't use.
x=2/sqrt3

f(0)=5
lim x-->5- is 110. Can't use this though because 5 is not included in the interval.
Since this is the largest of the three numbers, 2/sqrt3, 5, 110, there is no absolute max.
The local minimum is at x=2/sqrt3.

I don't know if this is right or if there are any local max or absolute minimum.

Please help.