Question

Find the maximum and minimum values of the function x​

Answer 1

Answer:

-infinity to +infinity

Answer 2

(1)The primary way to find extrema (maxima or minima) of functions is to use calculus. All extrema occur at critical values of the function -- those values where the first derivative is zero or fails to exist.

You find the first derivative, check each location where the derivative fails to exist. Then you set the first derivative equal to zero and solve for x. Once you have x, you evaluate the function at x to obtain the value.

You can use the first derivative test to check whether you have a local maximum, local minimum, or neither (occasionally an inflection point)

(2) You can locate extrema of some functions without calculus. For example, quadratics with a positive leading coefficient will have an absolute minimum, while quadratics with a negative leading coefficient have an absolute maximum. These extreme are located at the vertex of the parabola. The x coordinate of the extrema will be at  when the function is written in standard form 

(3) You could graph the function. Without calculus, or special cases like parabolas, you won't be able to prove you have an extremum, but you can get a reasonable approximation. With many graphing utilities you can locate an extremum on a stated interval