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Category: Differentiation

use-the-method-of-lagrange-multipliers-to-fond-the-extrema-of-f-x-y-z-24x-2-y-2-6-z-2-subject-to-z-x-2-y-2-2xy-

Question Number 131690 by LYKA last updated on 07/Feb/21 $${use}\:{the}\:{method}\:{of}\: \\ $$$$\boldsymbol{{lagrange}}\:\boldsymbol{{multipliers}}\:\boldsymbol{{to}}\:\boldsymbol{{fond}}\: \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{extrema}}\:\boldsymbol{{of}}\: \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{x}}.\boldsymbol{{y}}.\boldsymbol{{z}}\right)=\mathrm{24}\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{y}}^{\mathrm{2}} \left(\mathrm{6}−\boldsymbol{{z}}^{\mathrm{2}} \right) \\ $$$$\boldsymbol{{subject}}\:\boldsymbol{{to}}\:\boldsymbol{{z}}=\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{xy}} \\ $$$$…

What-is-the-maximum-area-of-ellipse-x-2-a-2-y-2-b-2-1-which-touches-the-line-y-3x-2-

Question Number 131642 by liberty last updated on 07/Feb/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{area}\: \\ $$$$\mathrm{of}\:\mathrm{ellipse}\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} }+\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }=\mathrm{1}\:\mathrm{which}\:\mathrm{touches} \\ $$$$\mathrm{the}\:\mathrm{line}\:\mathrm{y}\:=\:\mathrm{3x}+\mathrm{2}. \\ $$ Answered by benjo_mathlover last updated…

differentiate-y-10-1-sin-2-3x-

Question Number 66099 by olalekan2 last updated on 09/Aug/19 $${differentiate}\:{y}=\mathrm{10}^{\mathrm{1}−{sin}^{\mathrm{2}} \mathrm{3}{x}} \\ $$ Commented by mathmax by abdo last updated on 09/Aug/19 $${y}\left({x}\right)\:=\mathrm{10}^{\mathrm{1}−{sin}^{\mathrm{2}} \left(\mathrm{3}{x}\right)} \:\Rightarrow{y}\left({x}\right)\:={e}^{\left(\mathrm{1}−{sin}^{\mathrm{2}}…

Given-f-x-f-x-4-x-R-If-5-7-f-x-dx-T-3-5-f-x-dx-L-then-2-10-f-x-dx-

Question Number 131550 by liberty last updated on 06/Feb/21 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}+\mathrm{4}\right)\:\forall\mathrm{x}\in\mathbb{R} \\ $$$$\:\mathrm{If}\:\int_{\mathrm{5}} ^{\mathrm{7}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\:=\:\mathrm{T}\:;\:\int_{\mathrm{3}} ^{\mathrm{5}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\:=\:\mathrm{L} \\ $$$$\mathrm{then}\:\int_{\mathrm{2}} ^{\mathrm{10}} \mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=? \\ $$ Answered by talminator2856791…