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If the absolute maximum value of f(x) = 1/(|x| + 5) + 1/(|x - 5| + 5) is A, then find 10A.

1. 1
2. 2
3. 3
4. 4

Correct answer: 4

Solution

The function f(x) is symmetric about x = 2.5. At x = 0 or x = 5 it equals 3/10 = 0.3, while at x = 2.5 it equals 4/15 ≈ 0.267. Checking all critical points, the maximum value A = 2/5 occurs... recheck: at x=0, f = 1/5 + 1/10 = 2/10+1/10 = 3/10, so A = 3/10? But then 10A = 3. However the standard answer is 4 if A = 2/5. Let me recheck at x=0: 1/(0+5)+1/(5+5) = 1/5+1/10 = 3/10. The maximum is 3/10, so 10A = 3.

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