Given the function g(x) = b(−5x + 1)6 − a , where a ≠ 0 and b ≠ 0 are constants.

a. find g′(x) and g′′(x).

b. prove that g is monotonic (this means that either g always increases or g always decreases).

c. show that the x-coordinate(s) of the location(s) of the relative extrema are independent of a and b.