Question Number 180729 by sciencestudent last updated on 16/Nov/22
$${if}\:{f}\left({x}\right)=\frac{{kx}+\mathrm{3}}{\mathrm{2}{x}−\mathrm{5}}\:\:\:{is}\:{a}\:{constant}\:{function} \\ $$$${then}\:{what}\:{will}\:{be}\:{the}\:{value}\:{of}\:{k}? \\ $$
Answered by srikanth2684 last updated on 16/Nov/22
$${f}'\left({x}\right)=\mathrm{0} \\ $$$$\frac{{k}\left(−\mathrm{5}\right)−\left(\mathrm{3}\right)\left(\mathrm{2}\right)}{\left(\mathrm{2}{x}−\mathrm{5}\right)^{\mathrm{2}} }=\mathrm{0} \\ $$$$−\mathrm{6}=\mathrm{5}{k} \\ $$$$\frac{−\mathrm{6}}{\mathrm{5}}={k} \\ $$
Answered by mr W last updated on 16/Nov/22
$$\frac{{kx}+\mathrm{3}}{\mathrm{2}{x}−\mathrm{5}}={c} \\ $$$$\left({k}−\mathrm{2}{c}\right){x}+\mathrm{3}+\mathrm{5}{c}=\mathrm{0} \\ $$$$\mathrm{3}+\mathrm{5}{c}=\mathrm{0}\:\Rightarrow{c}=−\frac{\mathrm{3}}{\mathrm{5}} \\ $$$${k}−\mathrm{2}{c}=\mathrm{0}\:\Rightarrow{k}=−\frac{\mathrm{6}}{\mathrm{5}} \\ $$