Let f : (\R^2 → \R) be the function defined by f(x, y) = 8(x... | Mathematics | SolveeIt | Solveeit

Today, August 23

Question

Let f : $\R^2 → \R$ be the function defined by
f(x, y) = 8(x2 - y2) - x4 + y4.
Then which of the following statements is/are true ?

A

f has 9 critical points

B

f has a saddle point at (2, 2)

C

f has a local maximum at (−2, 0)

D

f has a local minimum at (0, −2)

Answer

f has 9 critical points

Explanation

Solution

The correct option is (A) : f has 9 critical points, (B) : f has a saddle point at (2, 2), (C) : f has a local maximum at (−2, 0) and (D) : f has a local minimum at (0, −2).