The value of a such that the area bounded by the curve y = x 2 + 2 a x + 3 a 2 , the coordinate axes and the line x = 1 , attains its least value is equal to

Question

The value of a such that the area bounded by the curve y = x 2 + 2 a x + 3 a 2 , the coordinate axes and the line x = 1 , attains its least value is equal to, 1 6, - 1 6, 1 3, - 1 3

MARKS App · Accepted Answer

y = x 2 + 2 a x + 3 a 2 is positive for all x ∈ R Area = ∫ 0 1 x 2 + 2 a x + 3 a 2 d x = 1 3 + 2 a 1 2 + 3 a 2 = 1 3 + a + 3 a 2 Area = 9 a 2 + 3 a + 1 3 Which is minimum at a = - 1 6

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