Final answer:
To find the smallest product of two numbers with a difference of 66, considering a negative and a positive number provides the minimum product, which would be -33 and 33 respectively, making the correct answer option b) Smaller: -33, Larger: 33.
Step-by-step explanation:
To find two numbers whose difference is 66 and whose product is a minimum, we need to consider how numbers combine through subtraction and multiplication. The numbers that come closest to being equal while still having a difference of 66 will lead to the smallest product - this is because the farther apart the numbers are, the larger the product becomes. The smallest product implies the two numbers must be as close to each other as possible given their difference. For positive numbers, this would be a symmetrical relationship around half of 66, which is 33. However, including negative numbers allows for the minimum product.
Considering negative numbers, the pair that would give the smallest product would be -33 and 33 because the product of two numbers with one being the negative counterpart of the other results in the smallest positive product when considering a fixed difference. Therefore, the correct answer would be:
- Smaller number: -33
- Larger number: 33
As a result, the correct option is:
b) Smaller: -33, Larger: 33