Explanation:
when you are on that level of math that you get this type of question - this is totally easy.
we get the extreme point(s) of a function by finding the zeros of the first derivative of the function.
f'(x) = 4x - 8
so,
0 = 4x - 8
8 = 4x
x = 2
to determine whether it is a minimum or a maximum, we have 2 choices :
the quick way for a quadratic (parabola) equation by looking at the factor of x² : is it >0, then the parabola opens up upwards, and the extreme point is therefore a minimum. if it is <0, then it opens downward, and the extreme point is a maximum.
in our case : 2 is larger than 0, therefore minimum.
or the formal way for any type of function : create the second derivative and see, if it is >0 (minimum) or <0 (maximum) for the extreme x.
in our case
f''(x) = 4
this is larger than 0 for all x, so the extreme point is a minimum.