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.

Question

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.

Philoid · Accepted Answer

It is given that f(x) = x⁴ – 62x² + ax + 9

Then, f’(x) = 4x³ – 124x+ a

It is given that function f attains its maximum value on the interval [0, 2] at x = 1.

⇒ f’(1) = 0

⇒ 4 – 124 + a = 0

⇒ a = 120

Therefore, the value of a is 120.

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.