Mathematics - Application of Derivative Question with Solution | TestHub

Surface area $\mathrm{A}$ of a cube of side $\mathrm{x}$ is given by $A=6x^2$, On differentiating w.r.t. $x$, we get $\frac{\mathrm{dA}}{\mathrm{dx}}=12\mathrm{x}$ Let the change in $x$ be $\Delta x=m\%$ of $x$ $=\frac{\mathrm{mx}}{100}$ Change in surface area, $\begin{array}{l}\Delta \mathrm{A}=\left(\frac{\mathrm{dA}}{\mathrm{dx}}\right)\Delta \mathrm{x}=(12\mathrm{x})\Delta \mathrm{x}\\ =12\mathrm{x}\left(\frac{\mathrm{mx}}{100}\right)=\frac{12{\mathrm{x}}^2\mathrm{m}}{100}\end{array}$ $\therefore$ The approximate change in surface area $\begin{array}{l}=\frac{2\mathrm{m}}{100}\times 6{\mathrm{x}}^2\\ =2\mathrm{m}\%\text{ of original surface area }\end{array}$