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Category: Differentiation

Find-minimum-value-of-function-f-x-2x-x-1-x-2-1-

Question Number 167167 by cortano1 last updated on 08/Mar/22 $$\:\:\mathrm{Find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\:\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}−\sqrt{\mathrm{x}+\mathrm{1}}−\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}} \\ $$ Answered by MJS_new last updated on 08/Mar/22 $${f}\left(−\mathrm{1}\right)=−\mathrm{2} \\ $$$${f}\:\mathrm{has}\:\mathrm{a}\:\mathrm{singularity}\:\mathrm{at}\:{x}=−\mathrm{1}…

Question-167158

Question Number 167158 by mnjuly1970 last updated on 08/Mar/22 Answered by mindispower last updated on 10/Mar/22 $${cos}\left(\mathrm{3}{n}\right)=\mathrm{4}{cos}^{\mathrm{3}} \left({n}\right)−\mathrm{3}{cos}\left({n}\right)\Rightarrow{cos}^{\mathrm{3}} \left({n}\right)=\frac{{cos}\left(\mathrm{3}{n}\right)+\mathrm{3}{cos}\left({n}\right)}{\mathrm{4}} \\ $$$$\Theta=\frac{\mathrm{1}}{\mathrm{4}}{Re}\left\{\underset{{n}\geqslant\mathrm{1}} {\sum}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{\mathrm{2}} }.\left({e}^{\mathrm{3}{in}} +\mathrm{3}{e}^{{in}}…

if-y-sin2x-is-the-solution-of-differintial-equation-d-2-y-dx-2-4y-k-then-the-k-is-

Question Number 101558 by mhmd last updated on 03/Jul/20 $${if}\:{y}={sin}\mathrm{2}{x}\:{is}\:{the}\:{solution}\:{of}\:{differintial}\:{equation}\: \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\mathrm{4}{y}={k}\:{then}\:{the}\:{k}\:{is}\:……. \\ $$ Answered by bemath last updated on 03/Jul/20 $$\mathrm{y}'=\mathrm{2cos}\:\mathrm{2x}\:\Rightarrow\mathrm{y}''=−\mathrm{4sin}\:\mathrm{2x} \\…

What-are-all-critical-point-for-f-x-y-2x-2-y-3-2xy-

Question Number 101510 by bemath last updated on 03/Jul/20 $$\mathrm{What}\:\mathrm{are}\:\mathrm{all}\:\mathrm{critical}\:\mathrm{point} \\ $$$$\mathrm{for}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\mathrm{2x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{3}} −\mathrm{2xy} \\ $$ Commented by bramlex last updated on 03/Jul/20 $$\left(\mathrm{1}\right)\frac{\partial\mathrm{f}}{\partial\mathrm{x}}\:=\:\mathrm{4x}−\mathrm{2y}=\mathrm{0}\:,\:\mathrm{y}\:=\:\mathrm{2x} \\…

Question-101291

Question Number 101291 by Mikael_786 last updated on 01/Jul/20 Answered by mr W last updated on 01/Jul/20 $$\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} \frac{{dy}}{{dx}}+{ay}+{ax}\frac{{dy}}{{dx}}=\mathrm{0} \\ $$$$\mathrm{6}{x}−\mathrm{6}{y}\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} +\left({ax}−\mathrm{3}{y}^{\mathrm{2}} \right)\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}}…

minimum-value-f-x-y-x-2-y-2-with-constrain-g-x-y-x-2-y-16-

Question Number 101258 by bemath last updated on 01/Jul/20 $$\mathrm{minimum}\:\mathrm{value}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{with}\:\mathrm{constrain}\:\mathrm{g}\left(\mathrm{x},\mathrm{y}\right)=\:\mathrm{x}^{\mathrm{2}} \mathrm{y}−\mathrm{16} \\ $$ Commented by john santu last updated on 01/Jul/20 $$\mathrm{f}\left(\mathrm{x},\mathrm{y},\lambda\right)=\mathrm{x}^{\mathrm{2}}…

Consider-a-square-based-pyramid-with-a-height-of-6x-cm-and-a-base-length-of-2-x-cm-Find-maximum-value-of-volume-of-pyramid-

Question Number 101182 by bemath last updated on 01/Jul/20 $$\mathcal{C}\mathrm{onsider}\:\mathrm{a}\:\mathrm{square}\:−\:\mathrm{based} \\ $$$$\mathrm{pyramid}\:\mathrm{with}\:\mathrm{a}\:\mathrm{height}\:\mathrm{of}\:\mathrm{6}{x}\:\mathrm{cm} \\ $$$$\mathrm{and}\:\mathrm{a}\:\mathrm{base}\:\mathrm{length}\:\mathrm{of}\:\left(\mathrm{2}−{x}\right)\mathrm{cm}. \\ $$$$\mathrm{Find}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{volume}\:\mathrm{of}\:\mathrm{pyramid}. \\ $$ Answered by bemath last updated…