Q73 / 120 · VITEEE 2018 · Mathematics
If at $x=1$, the function $x^{4}-62 x^{2}+a x+9$ attains its maximum value on the interval $[0,2]$, then the value of a is
- A110
- B10
- C55
- Correct answerDNone of these
Solution
Let $f(x)=x^{4}-62 x^{2}+a x+9$
$$
\Rightarrow \mathrm{f}^{\prime}(\mathrm{x})=4 \mathrm{x}^{3}-124 \mathrm{x}+\mathrm{a}
$$
It is given that function fattains its maximum value on the interval $[0,2]$ at $x=1$.
$$
\begin{array}{l}
\therefore \mathrm{f}^{\prime}(1)=0 \Rightarrow 4 \times 1^{3}-124 \times 1+1=0 \\
\Rightarrow 4-124+\mathrm{a}=0 \Rightarrow \mathrm{a}=120
\end{array}
$$
Hence, the value of a is 120 .
Hence, the correct answer is option: 'D'.