Differentiate:
2xy+x²(dy/dx)+4y³(dy/dx)=2, dy/dx=(2-2xy)/(x²+4y³).
At (-1,1) dy/dx=4/5. If we differentiate again d²y/dx²=[(x²+4y³)(-2x(dy/dx)-2y)-(2-2xy)(2x+12y²(dy/dx))]/(x²+4y³)².
At (-1,1) d²y/dx²=[(5)(8/5-2)-(4)(-2+48/5)]/25<0, implying gradient=⅘, maximum (concavity downwards), answer a.