Answer
$z = 4x-y-6$
Work Step by Step
Question:
$z = 2x^{2} + x^{2} -5y$ $(1,2,-4)$
The equation of the tangent plane to the surface is:
$z - z_{0} = f_{x}(x_{0},y_{0})(x - x_{0}) + f_{y}(x_{0},y_{0})(y - y_{0})$
$f_{x} = 4x$
so $f_{x}(1,2) = 4$
$f_{y} = 2y - 5$
so $f_{y}(1,2) = -1$
So the equation is:
$z + 4 = 4*(x-1) - 1(y-2)$
And the final answer is:
$z = 4x-y-6$
