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07/02/2022 12:30 pm
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If 'R' is the least value of 'a' such that the function f(x) = x2 + ax + 1 is increasing on [1, 2] and 'S' is the greatest value of 'a' such that the function f(x) = x2 + ax + 1 is decreasing on [1, 2], then the value of R S - is _________.
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07/02/2022 12:36 pm
f(x) = x2 + ax + 1
f'(x) = 2x + a
when ƒ(x) is increasing on [1, 2]
2x + a ≥ 0 ∀ x ∈ [1, 2]
a ≥ – 2x ∀ x ∈ [1, 2]
R = –4
when ƒ(x) is decreasing on [1, 2]
2x + a ≤ 0 ∀ x ∈ [1, 2]
a ≤ –2 ∀ x ∈ [1, 2]
S = -2
|R - S| = |-4 + 2| = 2