It is given that at x = 1, the function x^ 4 − 62x^ 2 + ax + 9 attains its maximum value, on the interval [0, 2]. Find the value of a.
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it is given that y = x⁴ - 62x² + ax + 9
differentiate it with respect to x ,
dy/dx = 4x³ - 124x + a
A/C to question, function f attains its maximum value on the interval [0, 2] at x = 1.
therefore , f’(1) = 0
⇒ 4(1)³ - 124(1) + a = 0
⇒ 4 – 124 + a = 0
⇒ a = 120
Therefore, the value of a is 120.
differentiate it with respect to x ,
dy/dx = 4x³ - 124x + a
A/C to question, function f attains its maximum value on the interval [0, 2] at x = 1.
therefore , f’(1) = 0
⇒ 4(1)³ - 124(1) + a = 0
⇒ 4 – 124 + a = 0
⇒ a = 120
Therefore, the value of a is 120.
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