Find the Absolute Maximum and Absolute Minimum of f on (0,3].

Question

f(x)=(x^3-4x^2+7x)/x
Multiple choice question
I know the minimum is (2,3) but the maximum is either nothing or (0,7) but I can't tell which one

Answer 1

on the given domain,

f(x) = x^2-4x+7
minimum is f(2)=3
limit as x->0 of f(x) = 7
f(3) = 4

So,
abs min = -9
abs max = 7
not strictly true, since f(0) is undefined, and there is no maximum number less than 7.

See the graph at

Answer 2

so, I guess the real(!) answer is indeed that there is no absolute max value.