I need to find the slope $\displaystyle \frac{dy}{dx}$ at the point P. The only thing I know is that:

$\displaystyle y = f(x)$

$\displaystyle \frac{dx}{dt} = v_0$ (constant)

The acceleration at P is: $\displaystyle \vec{a} = \frac{a}{\sqrt{2}}(\hat{t}+\hat{n})$ (a constant and > 0, natural coordinates)