Which of the following is the only local extremum for the function below?
f(x) = x_1 + x_2 + \frac{(x_1x_2)}{2} - x_1^2 - x_2^2
a. $(x_1, x_2) = (1, 1)$
b. $(x_1, x_2) = (2, 2)$
c. $(x_1, x_2) = (1/2, 1/2)$
d. $(x_1, x_2) = (2/3, 2/3)$
QUESTION 3
Which of the following statements concerning the extremum in the previous question are correct?
a. The extremum in the previous question is a local minimum.
b. The extremum in the previous question is a local maximum.
c. The extremum in the previous question is an inflection point.
d. The extremum in the previous question may be a local maximum, local minimum or inflection point.