If the function f ( x ) = 2 x 3 − 9 ax 2 + 12 a 2 x + 1 , where a 0 , attains its local maximum and local minimum values at p and q , respectively, such that p 2 = q , then f ( 3 ) is equal to:

Question

If the function f ( x ) = 2 x 3 − 9 ax 2 + 12 a 2 x + 1 , where a > 0 , attains its local maximum and local minimum values at p and q , respectively, such that p 2 = q , then f ( 3 ) is equal to:

TestHub · Accepted Answer

f ′ ( x ) = 6 x 2 − 18 a x + 12 a 2 f ′ ( x ) = 6 ( x 2 − 3 a x + 2 a 2 ) roots are a , 2 a p 2 = q ⇒ a 2 = 2 a a = 2 f ( x ) = 2 x 3 − 18 x 2 + 48 x + 1 f ( 3 ) = 37

Mathematics - Application of Derivative Question with Solution | TestHub

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