Provide an appropriate response.
-Find any local extrema (maxima, minima, or saddle points) of $f ( x , y )$ given that $f _ { x } = 8 x - 24$ and $f _ { y } = 2 y - 4$.
A) Local maximum at (3, 2)
B) Saddle point at (2, 3)
C) Local maximum at (2, 3)
D) Local minimum at (3, 2)

Question

Quizplus · Accepted Answer

To find local extrema, we first find the critical points by setting the first partial derivatives equal to zero: $f_x = 8x - 24 = 0$ and $f_y = 2y - 4 = 0$. Solving these equations gives $x = 3$ and $y = 2$, so the critical point is at (3, 2). Without the second partial derivatives, we cannot definitively classify this point, but given the options and the nature of the question, we infer that (3, 2) is a point of interest, and the correct answer is the one identifying the nature of this point correctly.

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

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