Find constants 'a' and 'b' in the function f(x) = a x x x eᵇ x x) such that f(1/2) = 1 and the function has a local maximum at x = 1/2.
a) a = 2, b = 1
b) a = 1, b = 2
c) a = 1/2, b = 1
d) a = 1, b = 1/2