Differentiating both sides with respect to [tex]x[/tex] gives
[tex]\dfrac{\mathrm d}{\mathrm dx}[2x^2+y^2]=\dfrac{\mathrm d}{\mathrm dx}17[/tex]
[tex]4x+2y\dfrac{\mathrm dy}{\mathrm dx}=0[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{4x}{2y}=-\dfrac{2x}y[/tex]
Differentiating again, we get
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=-\dfrac{2y-2x\frac{\mathrm dy}{\mathrm dx}}{y^2}[/tex]
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{2x\left(-\frac{2x}y\right)-2y}{y^2}[/tex]
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=-\dfrac{4x^2-2y^2}{y^3}[/tex]
Plug in [tex]x=2[/tex] and [tex]y=3[/tex] and you're done.
