Find the absolute maximum and absolute minimum of f on the interval (0,3] when f(x)=(x^3-4x^2+7x)/x

A. max:none, min: (3,4)

B. max(0,7), min3,4)

C. max: none, min: (2,3)

D. max (0,7), min: (2,3)

E. none of the above

I found the derivative, 2x-4

the critical number, 2

and plugged in these values into f, to see which gives the highest and lowest value.

we dont plug in 0 because its (0,3] and not [0,3].

f(2) = 3

f(3) = 4

However, the correct answer is C max:none, and min2,3).

I dont get why there is no maximum, when clearly, when (3,4) and also (1,4) are values in the interval