Do you not understand the meaning of the words "maximum" and "minimum"? If they both have the same value for f, then you can't have one the maximum and the other a minimum. Although it is quite possible that neither is a maximum or minimum.
There is a theorem saying that a continuous function will achieve both max and min on a compact set (closed and bounded interval will work). Further there is a theorem saying that they must lie either inside the interval, where the derivative is 0, or on the boundary. So it is possible that (1, 1) and (-1, -1) both give a maximum value while the minimum occurs at x= -10 or 10. Or that both (1, 1) and (-1, -1) both give a minimum value while the maximum occurs at x= -10 or 10. Or that the maximum occurs at either x= -10 or x= 10 or the other way around. To tell, evaluate f at those points and see which is the largest and which is the smallest!