Question Number 26774 by NECx last updated on 29/Dec/17
$${If}\:{one}\:{side}\:{of}\:{a}\:{square}\:{reduces}\:{by} \\ $$$$\mathrm{10\%}\:{and}\:{the}\:{adjacent}\:{side}\:{increases} \\ $$$${by}\:\mathrm{30\%}.{Using}\:{the}\:{application}\:{of} \\ $$$${differentiationfind}\:{the}\:\%\:{change} \\ $$$${in}\:{the}\:{area}\:{of}\:{the}\:{square}. \\ $$
Commented by NECx last updated on 30/Dec/17
$${please}\:{help} \\ $$
Commented by prakash jain last updated on 30/Dec/17
$${A}={lb} \\ $$$$\frac{{dA}}{{dt}}={b}\frac{{dl}}{{dt}}+{l}\frac{{db}}{{dt}} \\ $$$${initially}\:{l}={b}\:{and}\:{A}={b}^{\mathrm{2}} \\ $$$$\frac{{db}}{{dt}}=−.\mathrm{1}{b} \\ $$$$\frac{{dl}}{{dt}}=+.\mathrm{3}{l} \\ $$$$\frac{{dA}}{{dt}}={b}×.\mathrm{3}{l}−{l}×.\mathrm{1}{b}=.\mathrm{2}{lb}=.\mathrm{2}{A} \\ $$$$\mathrm{Area}\:\mathrm{will}\:\mathrm{increase}\:\mathrm{by}\:\mathrm{20\%} \\ $$
Commented by NECx last updated on 31/Dec/17
$${wow}....\:{this}\:{is}\:{wonderful} \\ $$
Commented by prakash jain last updated on 31/Dec/17
$$\mathrm{Since}\:\mathrm{the}\:\mathrm{question}\:\mathrm{asked}\:\mathrm{for}\:\mathrm{use} \\ $$$$\mathrm{of}\:\mathrm{derivate}\:\mathrm{i}\:\mathrm{answered}\:\mathrm{as}\:\mathrm{in}\:\mathrm{comment}. \\ $$$$\mathrm{I}\:\mathrm{assumed}\:\mathrm{30\%}\:\mathrm{and}\:\mathrm{10\%}\:\mathrm{question}\: \\ $$$$\mathrm{as}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{change}. \\ $$
Commented by NECx last updated on 02/Jan/18
$${its}\:{really}\:{nice}....\:{I}'{ve}\:{always} \\ $$$${tjought}\:{of}\:{it}\:{but}\:{have}\:{never}\:{known} \\ $$$${how}\:{to}\:{apply}\:{it}\:{until}\:{now}. \\ $$