Answer
$L(x,y) = x+1/4y$
Work Step by Step
Question:
$f(x,y) = \sqrt {xy}$, $(1,4)$
The equation of the linearization function:
$L(x,y) = f(a,b) + f_{x}(a,b)(x - a) + f_{y}(a,b)(y - b)$
$f(1,4) = 2$
$f_{x} = 1/2*\sqrt {xy} * y$ = $y/{2\sqrt {xy}}$
so $f_{x}(1,4) = 1$
$f_{y} = 1/2*\sqrt {xy} * x$ = $x/{2\sqrt {xy}}$
so $f_{y}(1,4) = 1/4$
So the equation is:
$L(x,y) = 2 +(x-1) +1/4* (y-4)$
And the final answer is:
$L(x,y) = x+1/4y$
