For each of the regions D in R^2 below, fill in the blank so that the statements are true: A continuous function on D= {(x, y) ∈ R^2 | 2x^4+6y^2 >= 152} have an absolute maximum.

a. must
b. might or might not
c. must not

b. might or might not

Step-by-step explanation:

Theorem:

If f is a continuous function in a bounded interval, it must have an absolute maximum.

In this question:

The interval is  2x^4+6y^2 >= 152, which goes to infinite, meaning it is not bounded, and so the function might or might not have an absolute maximum, and the correct answer is given by option b.

b. might or might not

Step-by-step explanation:

For each of the regions D in R^2 below, fill in the blank so that the statements are true: might or might not

answer is 144

step-by-step explanation: