the limit as x goes to 0 is 7 which is bigger than 4. Since 0 is not in the interval there is no max . Note there are an inifinity of values of x near 0 which are greater than 4.
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