Trying to find the right answer to this..

Let f (x) = x 4 – 62x 2 + ax + 9 f ' (x) = 4x 3 – 124x + a ∴ f ' (1) = 4 – 124 + a = – 120 + a ∴ f (x) attains max. value at x = 1 ∴ f ' (1) = 0 ⇒ – 120 + a = 0 ⇒ a – 120.

Application of Derivatives

Question

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It is given that at x = 1, function x⁴ – 62x² + ax + 9 attains its maximum value, on the interval [0, 2], Find the value of a.

Answer

Let f (x) = x⁴ – 62x² + ax + 9
f ' (x) = 4x³– 124x + a
∴ f ' (1) = 4 – 124 + a = – 120 + a
∴ f (x) attains max. value at x = 1
∴ f ' (1) = 0 ⇒ – 120 + a = 0 ⇒ a – 120.