Given the function below, where a, b, c, d, e are constants.

f(x) = ax^4 + bx^3 + cx^2 + dx + e

How do I get the minimum return value given that x lies in the range 0 <= x < 1?

I know this has something to do with differentiation (maybe??), and I know that the derivative is:

df(x) = 4ax^3 + 3bx^2 + 2cx + d

But I have no idea how to get the minimum value back within a given range of x.

Any help would be appreciated!