Maxima and MinimaHard
Question
If x is real, the maximum value of 
is
is Options
A.1/4
B.41
C.1
D.17/7
Solution
y =
3x2(y - 1) + 9x(y - 1) + 7y - 17 = 0
D ≥ 0 ∵ x is real
81(y - 1)2 - 4x3(y - 1)(7y - 17) ≥ 0
⇒ (y - 1) (y - 41) ≤ 0 ⇒ 1 ≤ y ≤ 41.
3x2(y - 1) + 9x(y - 1) + 7y - 17 = 0
D ≥ 0 ∵ x is real
81(y - 1)2 - 4x3(y - 1)(7y - 17) ≥ 0
⇒ (y - 1) (y - 41) ≤ 0 ⇒ 1 ≤ y ≤ 41.
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