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 __________ have an absolute maximum. a. must …

Question

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= 2x^4+6y^2 >= 152 __________ have an absolute maximum.

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

Answer 1

b. might or might not

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 2

b. might or might not

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.