Question

4. When the second derivative test (SDT) is used for a critical point the result can be local maximum, local minimum, saddle point or test inconclusive. Consider the function f(x, y) = y 2 − 2y cos(x) with domain restricted to {(x, y) | −1 ≤ x ≤ 4 and − 2 ≤ y ≤ 4} and the three points P = ( π 2 , 0) Q = (0, 1) and R = (π, −1).

(a) Find all the critical points of f in the domain. The answer is ”P, Q, R and no others.” But you need to do the work to show that without knowing P, Q, R in advance.

(b) What does the SDT tell us about P ?

(c) What does the SDT tell us about Q ?

(d) What does the SDT tell us about R ? Make sure I see all the work needed to support your answers.

Answer 1