
Michael P. answered 01/15/16
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Ryan,
You prove both postulates using the derivative (or differential) of a sum (or difference):
d(h +/- g)/dx = dh/dx +/- dg/dx
Since h and g have a relative maximum at x0, dh/dx = 0 at x=x0 and dg/dx = 0 at x = x0.
d(h +/- g)/dx = 0 +/- 0 = 0 at x=x0 and, thus, h +/- g has a relative maximum at x0.
Michael.