Mathematics - Application of Derivative Question with Solution | TestHub

Let $f(x)=x^4-62x^2+ax+9$ $$\Rightarrow {\mathrm{f}}^{\prime }(\mathrm{x})=4{\mathrm{x}}^3-124\mathrm{x}+\mathrm{a}$$ 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 .