(a) \(\dfrac{dy}{dx}=e^{-x^2/4}(1-x^2/2)\). It vanishes at \(x=\sqrt2\), and changes from positive to negative there. Hence \(\boxed{M=(\sqrt2,\sqrt2e^{-1/2})}\).

(b) With \(u=x^2\), \(dx=\dfrac1{2\sqrt u}\,du\), and the limits become 0 and 9. Thus \(A=\tfrac12\int_0^9e^{-u/4}\,du=[-2e^{-u/4}]_0^9=\boxed{2-2e^{-9/4}}\).