(a) It is given that function f ( x )= x^4-62 x^2+a x +9 attains local maximum value at x =1. Find the value of ' a ', hence obtain all other points…

Let length of rectangle be $\displaystyle \mathrm{x}$ cm and breadth be $\displaystyle (150-\mathrm{x}) \mathrm{cm}$. Let $\displaystyle r$ be the radius of cylinder $\displaystyle \Rightarrow 2 \pi r=\mathrm{x} \Rightarrow r=\frac{\mathrm{x}}{2 \pi}$ $$V=\pi r^{2} h=\pi\left(\frac{\mathrm{x}^{2}}{4 \pi^{2}}\right)(150-\mathrm{x})=\frac{75 \mathrm{x}^{2}}{2 \pi}-\frac{\mathrm{x}^{3}}{4 \pi} $$ Length of rectangle is $\displaystyle 100$ cm and breadth of rectangle is $\displaystyle 50$ cm .