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If a ≤ x ≤ b and c ≤ y ≤ d, how to find the maximum and minimum values for xy?

A) Max: ac, Min: bd
B) Max: bd, Min: ac
C) Max: ad, Min: bc
D) Max: bc, Min: ad

1 Answer

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Final answer:

The maximum value of xy is achieved by multiplying the largest values b and d, resulting in bd, and the minimum value is obtained by multiplying the smallest values a and c, resulting in ac.

Step-by-step explanation:

To find the maximum and minimum values for xy given the constraints a ≤ x ≤ b and c ≤ y ≤ d, you need to consider the possible products of the extreme values of x and y. The maximum value of xy will occur when you multiply the largest possible values of x and y, which is b and d respectively, resulting in bd.

Conversely, the minimum value of xy will occur when you multiply the smallest possible values of x and y, which is a and c respectively, giving the product ac. Therefore, the correct answer is B) Max: bd, Min: ac.

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