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y-x-2-17x-56-x-2-y-min-




Question Number 122379 by bounhome last updated on 16/Nov/20
y=((x^2 +17x−56)/(x−2))  y_(min) =...?
$${y}=\frac{{x}^{\mathrm{2}} +\mathrm{17}{x}−\mathrm{56}}{{x}−\mathrm{2}} \\ $$$${y}_{{min}} =…? \\ $$
Answered by MJS_new last updated on 16/Nov/20
y′=((x^2 −4x+22)/((x−2)^2 ))=0 no real solutions ⇒        ⇒ no local min/max  lim_(x→2^− )  y =+∞  lim_(x→2^+ )  y =−∞  ⇒ −∞<y<+∞
$${y}'=\frac{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{22}}{\left({x}−\mathrm{2}\right)^{\mathrm{2}} }=\mathrm{0}\:\mathrm{no}\:\mathrm{real}\:\mathrm{solutions}\:\Rightarrow\: \\ $$$$\:\:\:\:\:\Rightarrow\:\mathrm{no}\:\mathrm{local}\:\mathrm{min}/\mathrm{max} \\ $$$$\underset{{x}\rightarrow\mathrm{2}^{−} } {\mathrm{lim}}\:{y}\:=+\infty \\ $$$$\underset{{x}\rightarrow\mathrm{2}^{+} } {\mathrm{lim}}\:{y}\:=−\infty \\ $$$$\Rightarrow\:−\infty<{y}<+\infty \\ $$

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