Difficult# Laws of Motion: When Will the Penguin Slip?

APPHMC-EJA1VZ

A penguin is situated on an icy slope which has shape $y(x) = 0.95- x^2 / 12$ where $x$ is the distance away from the center of the slope (in meters).

If the penguin, which is initially at $x = 0$, starts to ever so slowly walk away towards the positive $x$ direction, at which $x$ coordinate will it lose traction and start to slip?

Ignore the effect of the penguin's motion, and assume the only factor relevant is where it is on the slope. Take the coefficient of friction between the penguin's feet and the icy slope to be $\mu_{static} = 0.2$.