I have a very tiny block that slides down a ramp in the Cartesian plane from point \(a\) to point \(b\). This ramp can be modelled by the function \(f(x)\) for \(x_a\leq x \leq x_b\). For all values of c such that \(a<c \leq b\), \(f(c)<f(a)\). If the block manages to slide from point \(a\) to \(b\). Prove that the maximum velocity of the block at point \(b\) is achieved when \(f(x)\) is a straight line from \(a\) to \(b\) if friction is present.
I will post the proof for this if no one has within 48 hours.