Question

If at $x = 1$, the function $x^4 - 62x^2 + ax + 9$ attains its maximum value on the interval $[0, 2]$, then the value of $a$ is

• A. 110
• B. 10
• C. 55
• D. None of these

Answer 1

Answer: (D)

Let $f(x) = x^4 - 62x^2 + ax + 9$
$\Rightarrow f '\left(x\right) = 4x^{3} - 124x + a$
It is given that function f attains its maximum value on the interval $\left[0,2\right]$ at $x = 1$.
$\therefore f'\left(1\right) =0 \Rightarrow 4 \times1^{3}-_{ }12^{4} \times 1 + 1 = 0$
$\Rightarrow 4 - 124 + a = 0 \Rightarrow a = 120$
Hence, the value of a is $120.$