# Optimization in mechanics

We have a curved plane which has a side view of a continous and double differential curve $$f:[0,1] \rightarrow [0,1],y=f(x)$$ with $$y(0)=0 , y(1)=1$$ and $$\dfrac{dy}{dx} \ge 0 , \dfrac{{d}^{2}y}{dx^{2}} \ge 0$$

In this co-ordinate system $$1$$ unit = $$1$$ metre. Also gravity is present in the $$-y$$ direction having a value of $$10 m/s^{2}$$.

An point object is released from the point $$(1,1)$$ on the plane and it takes time $$t$$ to reach the leave the plane from the bottom.

Let the minimum value of $$t$$ be $$t_{min}$$.

Find $$\lfloor 1000t_{min} \rfloor$$

The plane is smooth there is no friction present.You may use any computer software you want, any possible resources.

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