If the function f ( x ) = 2 x 2 − 9 a x 2 + 12 a 2 x + 1 , where a 0 , attains its maximum and minimum at p and q respectively such that p 2 = q , then a equals

Question

If the function f ( x ) = 2 x 2 − 9 a x 2 + 12 a 2 x + 1 , where a > 0 , attains its maximum and minimum at p and q respectively such that p 2 = q , then a equals

TestHub · Accepted Answer

f ( x ) = 2 x 3 − 9 a x 2 + 12 a 2 x + 1 f ′ ( x ) = 6 x 2 − 18 a x + 12 a 2 ; f ′′ ( x ) = 12 x − 18 a For max. or min. 6 x 2 − 18 a x + 12 a 2 = 0 ⇒ x 2 − 3 a x + 2 a 2 = 0 x = a or x = 2 a , at x = a max.and at x = 2 a min . p 2 = q a 2 = 2 a ⇒ a = 2 or a = 0 but a > 0 , therefore, a = 2 .

Mathematics - Application of Derivative Question with Solution | TestHub

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