Provide an appropriate response.
-Find any local extrema (maxima, minima, or saddle points) of $f ( x , y )$ given that $f _ { X } = 49 x ^ { 2 } - 49$ and $f _ { y } = 3 y + 6$
A) Local maximum at (1, -2); saddle point at (-1, -2)
B) Local minimum at (-1, -2); saddle point at (1, -2)
C) Local minimum at (1, -2); saddle point at (-1, -2)
D) Local maximum at (-1, -2); saddle point at (1, -2)

Question

Quizplus · Accepted Answer

The critical points are found by setting $f_x = 0$ and $f_y = 0$, giving points (1, -2) and (-1, -2). The second derivative test shows (1, -2) is a local minimum and (-1, -2) is a saddle point.

Provide an Appropriate Response f(x,y)f ( x , y )f(x,y) Given That

Provide an Appropriate Response $f ( x , y )$ Given That