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Question-50764




Question Number 50764 by Tawa1 last updated on 19/Dec/18
Commented by mr W last updated on 20/Dec/18
f(x)=(((x^2 +1)^6 −x^(12) −2x^6 )/(x^7 +x^5 +x^9 +x^3 ))  lim_(x→+∞)  f(x)=−∞  lim_(x→−∞)  f(x)=+∞  ⇒there is no maximum or minimum.
$${f}\left({x}\right)=\frac{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{6}} −{x}^{\mathrm{12}} −\mathrm{2}{x}^{\mathrm{6}} }{{x}^{\mathrm{7}} +{x}^{\mathrm{5}} +{x}^{\mathrm{9}} +{x}^{\mathrm{3}} } \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:{f}\left({x}\right)=−\infty \\ $$$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:{f}\left({x}\right)=+\infty \\ $$$$\Rightarrow{there}\:{is}\:{no}\:{maximum}\:{or}\:{minimum}. \\ $$
Commented by Tawa1 last updated on 20/Dec/18
God bless you sir
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

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