Adjust a one dimensional Bezier-Curve?

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I really need to adjust my one dimensional Bezier-Curve, but I don't know how.

I got this equation: $$ y = A(1-x)^3 + 3B(1-x)^2x + 3C(1-x)x^2 + Dx^3 $$ with the constants A,B,C,D which represent the $y$-value of my 4 control points.

But how can I make my y grow faster at the beginning? The end should be the same as before. I have no $x$-control-value in my equation to adjust that property.

Edit: My derivative at the beginning and at the end is equal zero. So:

y'(0)=0

y'(1)=0

I hope you understand my problem.

Thank you for helping me :)