Is (0, 0)a critical point of the following function? $f ( x , y ) = \cos x \cos y$
A)No.
B)Yes: (global)maximum.
C)Yes: local minimum.
D)Yes: (global)minimum.

Question

Quizplus · Accepted Answer

A critical point occurs where the first derivatives of a function with respect to all variables are zero or undefined. For $f(x, y) = \cos x \cos y$, the partial derivatives are $f_x = -\sin x \cos y$ and $f_y = -\sin y \cos x$. At (0, 0), both derivatives are 0, making it a critical point. To determine its nature, we can observe that $\cos x \cos y$ reaches its maximum value of 1 at (0, 0), since the maximum value of cosine is 1. Therefore, (0, 0) is a global maximum.

Is (0, 0)a Critical Point of the Following Function f(x,y)=cos⁡xcos⁡yf ( x , y ) = \cos x \cos yf(x,y)=cosxcosy

Is (0, 0)a Critical Point of the Following Function $f ( x , y ) = \cos x \cos y$