Menu Close

Category: Differentiation

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…

Calculate-If-0-1-tanh-1-x-3-x-dx-2-then-M-N-

Question Number 166690 by mnjuly1970 last updated on 25/Feb/22 $$ \\ $$$$\:\:\:\:\:\:\:\:\:{Calculate}\: \\ $$$$\:\:\:\:\:{If}\:\:,\:\boldsymbol{\phi}=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{tanh}^{\:−\mathrm{1}} \left(\:{x}^{\:\mathrm{3}} \:\right)}{{x}}\:{dx}\:=\:\alpha.\zeta\left(\:\mathrm{2}\right)\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{then}\:,\:\:\:\:\:\alpha\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:\mathscr{M}.\mathscr{N}\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−− \\ $$$$ \\…