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Question
It is given that at x = 1, the function x4− 62x2 + ax + 9 attains its maximum value, on the interval [0, 2]. Find the value of a.
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Solution
f (x) = x4 - 62x2 + ax + 9, 0 ≤ x ≤ 2
= f' (x) = 4x3 - 124x + a
We have f (x) attains maximum value at x = 1 ∈ [0, 2]
∴ We must have f' (1) = 0
⇒ 4 - 124 + a = 0
= a = 120
Thus, we have f(x) = x4 - 62x2 + 120x + 9
f (0) = 9, f(1) = 1 - 62 + 120 + 9 = 68 and
f (2) = 24 - 62 × 22 + 120 × 2 + 9 = 17
Clearly, f(x) is maximum at x = 1.
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