I have the function $2x^2+y$ and one constraint $x-y^2=1$ and want to find maximum value by lagrange multiplier. Intuitively, I see the point $(2,1)$ satisfies $c$ and have value of $f(2,1)=9$.

Using Lagrange function $f(z)-\lambda c(z)$, I get $\lambda^3-4\lambda^2-1$ thus $\lambda=4.06$. However, when plug this into the derivatives of $x$ and $y$ I got different values in particular $x=\frac{4.06}{4}=1.015$ which is much lower than $2$. Am I missing something here?