what-are-critical-points-of-this-function-z-xy-5xy-2-10y-

Question Number 96185 by bemath last updated on 30/May/20

what are critical points of this

function z = xy + {5 xy}^{2} + 10 y

Answered by john santu last updated on 30/May/20

(1) \frac{\partial z}{\partial x} = y + 5 y^{2} = 0

y (1 + 5 y) = 0 {\begin{cases} y = 0 \\ y = - \frac{1}{5} \end{cases}

(2) \frac{\partial z}{\partial y} = x + 10 x y + 10 = 0

\Rightarrow x (1 + 10 y) = - 10 .

if y = 0 \Rightarrow x = - 10

if y = - \frac{1}{5} \Rightarrow x = 10

c r i t i c a l p o i n t a r e (- 10, 0);

(10, - \frac{1}{5}) .