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

Question

The value of the parameter ‘a' such that the area bounded by y = a 2 x 2 + a x + 1 , coordinate axes and the line x = 1 attains its least value, is equal to, - 1 4, - 1 2, - 3 4, - 1

MARKS App · Accepted Answer

a 2 x 2 + a x + 1 is positive for all real values of x . ∴ Area = ∫ 0 1 a 2 x 2 + a x + 1 d x = a 2 3 + a 2 + 1 = 1 6 2 a 2 + 3 a + 6 = 1 6 2 a 2 + 3 2 a + 9 16 + 6 - 18 16 = 1 6 2 a + 3 4 2 + 39 8 , which is minimum for a = - 3 4

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