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