finding the value of x such that the vertical

Question

Finding the value of x such that the vertical distance is maximum. 

Conjecture consider the functions f(x) = ½ x² and g(x) = 1/16 x⁴ - ½ x² on the domain [0,4].Write the vertical distance d between the functions as a function of x and use calculus to find the value of x for which d is maximum.