SOLUTION: -3 is less than or equal to a, and a is less than or equal to 1. b = 4 - a^2 Using the facts above, what number is obtained when the smallest possible value of b is subtracted

Question 472224: -3 is less than or equal to a, and a is less than or equal to 1.
b = 4 - a^2
Using the facts above, what number is obtained when the smallest possible value of b is subtracted from the largest possible value of b?
Please explain, I do not understand. Thank you!
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Since a^2 is always nonnegative, for large-magnitude values of a, 4 - a^2 will decrease the value of b. To find the maximum value for b, we find the minimal value of a^2, which occurs when a = 0. This implies the maximum value of b is 4.

To minimize b, we maximize a^2 by setting a = -3 (the number contained in the domain with the highest absolute value). The least possible value of b is 4 - (-3)^2 = -5.

Hence the difference between the two is 4 - (-5) = 9.
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