I have a quartic function y=ax^4 + bx^3 + cx^2 + dx + e(a != 0). what is the best way to find max when 0.0 <= x <= 1.0

Question

how do i find the maximum value of a quartic function when x is in range between 0 and 1. solving 0 = 4ax^3 + 3bx^2 + 2cx + d to get possible candidate for maximum value is not