# Let's do some calculus! (46)

Calculus Level 5

If the maximum value of

$\large f(x,y,z) = 2x^2 + 3y - 4z$

subject to the constraints

$\begin{cases} 2x-4y-2z=5 \\ x^2+y^2 = 1 \end{cases}$

is equal to $$M$$, then evaluate $$\left\lfloor M \right\rfloor$$.

Note: It is advised to take the aid of a calculator for mathematical computations in this problem.