Automotive Engineering (Suspension Camber & Curvature Analysis)

An automotive chassis and suspension engineer is designing a performance double-wishbone suspension linkage for an electric sports vehicle. As the vehicle corners aggressively over bumps, the tire contact patch moves along an implicit non-linear curve relative to the subframe:

where $x$ is the horizontal track width change (in decimeters, $\text{dm}$) and $y$ is the vertical suspension travel (in $\text{dm}$). The vehicle's static ride-height baseline is calibrated at $(x, y) = (2, 2)$.

1. Use implicit differentiation to calculate the instantaneous slope $\frac{dy}{dx}$ of the suspension travel path at the baseline configuration $(2, 2)$.
2. Apply the Quotient Rule and back-substitution to calculate the second derivative $\frac{d^2y}{dx^2}$ at $(2, 2)$.
3. Interpret what the sign and numerical magnitude of $\frac{d^2y}{dx^2}$ tell the engineer regarding tire camber recovery and vehicle cornering grip.