# Quiz 10

$Consider~the~function~z=-x^{2}+3xy+x+4y-y^{2}.~Find~the~stationary~point.~$

$Consider~the~function~z=-x^{2}+3xy+x+4y-y^{2}.~Find~the~second~order~partial~derivatives.~$

$Consider~the~function~z=-x^{2}+3xy+x+4y-y^{2}.~Find~the~cross~partial~derivatives.~$

$Consider~the~function~z=-x^{2}+3xy+x+4y-y^{2}.~Find~the~maximum~point.~$

$Consider~the~function~z=-x^{2}+xy-2x+5y-2y^{2}.~Find~the~stationary~point.~$

$Consider~the~function~z=-x^{2}+xy-2x+5y-2y^{2}.~Find~the~maximum~point.~$

$Consider~the~function~z=x^{2}+xy-2x+4y-2y^{2}.~Find~the~stationary~point.~$

$Consider~the~function~z=x^{2}+xy-2x+4y-2y^{2}.~Find~the~saddle~point.~$

$Find~the~differential~(dz)~of~z=x^{2}+xy+x+2y+y^{2}.$

$Find~the~differential~(dz)~of~z=x^{2}+xy+x+2y+y^{2}.$

$Find~the~differential~(dY)~of~the~production~function,~Y=5L^{\frac{3}{4}}K^{\frac{1}{4}}.$

$From~the~differential~(dY)~of~the~production~function,~Y=5L^{\frac{3}{4}}K^{\frac{1}{4}},~find~the~slope~of~the~isoquant,~\frac{dK}{dL}.$

$Consider~the~production~function,~Y=5L^{\frac{3}{4}}K^{\frac{1}{4}}.~From~the~values~of~the~partial~derivatives~-~f_{L} ~and~f_{K},~find~the~slope~of~the~isoquant,~\frac{dK}{dL}.$

$Consider~the~function,~x^{3}-2x^{2}+4x+2xy+2y-3y^{2}+y^{3}=0.~Find~the~derivative,~\frac{dy}{dx},~by~implicit~differentiation.$

$Consider~the~function,~e^{2x}+\ln3y=0.~Find~the~derivative,~\frac{dy}{dx},~by~implicit~differentiation.$

$Consider~the~function,~x^{2}+y^{2}=4,~which~represents~a~circle~with~the~radius~of~2.~Find~the~slope~of~the~tangent~to~the~circle~using~the~$$~implicit~differentiation~rule.$

$Consider~the~function~z=2x+\ln~y,~where~y~=~3x+1.~Find~the~total~derivative~of~z~with~respect~to~x.$

$Consider~the~function~z=x^{2}+2y ~,~where~y=3\ln~x.~Find~the~total~derivative~of~z~with~respect~to~x.$

$Consider~the~function~z=10\sqrt{xy},~where~y=\ln~x.~Find~the~total~derivative~of~z~with~respect~to~x.$

$~The~inverse~demand~function~is~p~=~100~-~0.8q~(where~p~is~price~and~q~is~quantity).~Find~the~MR~(marginal~revenue)~in~q,~using~the~total~$$differentiation~on~the~total~revenue.$

$There~is~a~monopoly~firm~which~faces~a~market~demand~of~q~=~100~-~0.8p~(where~q~is~quantity~and~p~is~price).~Find~the~MR~(marginal~revenue)~$$~in~p,~using~the~total~differentiation~on~the~total~revenue.$
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