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 gives \[ \boxed{D=0,} \] the test is inconclusive. Always inspect the sign of the function around the stationary point. If it changes sign, the point is neither a maximum nor a minimum (typically a saddle-type point).

Answer 1

The Correct Option is D