Global Mins/maxes; Local Mins/maxes

Exactly what definition of "minimum" and "maximum" are you using? The standard definitions are simply that a function, f(x), has a "maximum" at a given value of x if and only if f(x) is larger than or equal to values of f at other values of x- "global" if f(x) is larger than or equal to f(y) for all y not equal to x and "local" if that is true for all y, other than x, in some region around x. There is no requirement that a function be differentiable or even continuous in order that a specific point give a max or min.

For example, define f(x) to be equal to 2 for all x except x= 3 and x= 4, f(3)= 0, f(4)= 7. The clearly f(x) has a maximum, 7, at x= 4 and a minimum, 0, at x= 3.

In your example, there are local maxima at x= 0, 3, and 8, local minima at x= 2 and 5, and the absolute maximum value is 7.

(Notice that the first two questions as where the max and min occur so ask for x values while the last question asks for the maximum value for the function.)
 
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