Question

Consider the function \( f(x,y) = (x - 2)^2(y + 3) \). Then:

• A. (2,-3) is not a stationary point of \( f \).
• B. \( f \) has a local minimum at (2,-3).
• C. \( f \) has a local maximum at (2,-3).
• D. \( f \) has neither a local maximum nor a local minimum at (2,-3).

Hint:

If the second derivative test \( D = f_{xx}f_{yy} - (f_{xy})^2 \) equals 0, the test is inconclusive. In such cases, look at the sign of the function relative to its value at the stationary point to identify saddle points.

Answer 1

The Correct Option is D