Question

6.

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.​

Answer 1

The value of a is 120.

Explanation:

Given function;

f(x) = x⁴ - 62x² + ax + 9

find the derivative of the function;

f'(x) = 4x³ - 124x + a

The function (f) attains its maximum value on the interval [0, 2], at x = 1.

f'(1) = 0

0 = 4(1)³ - 124(1) + a

0 = 4 - 124 + a

0 = -120 + a

120 = a

Thus, the value of a is 120.