Inequalities - Optimization Problems

$$-6 \le x \le 3$$ $$\displaystyle -4 \le y \le 1$$ What is the minimum value of _xy_?

Incorrect. You may have gotten this answer if you found the maximum, instead of the minimum, of _xy_. [[snippet]]

Incorrect. You may have gotten this answer if you found the second-lowest of the four products of the extremes instead of the lowest value of it. [[snippet]]

Incorrect. You might have gotten this answer if you found the minimum of _x_ + _y_ instead of _xy_. [[snippet]]

You are right! [[snippet]] You should get the following list. - $$(-6)(-4) = 24$$ - $$(-6)(1) = -6$$ - $$(3)(-4) = -12$$ - $$(3)(1) = 3$$ In this list, notice that the minimum value is –12. This makes sense. Since _xy_ can be negative, you will get the minimum by multiplying a negative number by a positive number in either order.

Incorrect. You might have gotten this answer if you made a mistake multiplying positive and negative numbers. Remember, the product of two negative numbers is positive. [[snippet]]

-24

-12

-10

-6

24