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Question Number 135211 by benjo_mathlover last updated on 11/Mar/21

Find minimum value of function  f(x) = ((4x^2 +8x+13)/(6(1+x)))

$$\mathrm{Find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{4x}^{\mathrm{2}} +\mathrm{8x}+\mathrm{13}}{\mathrm{6}\left(\mathrm{1}+\mathrm{x}\right)} \\ $$

Commented by mr W last updated on 11/Mar/21

lim_(x→−1^− ) f(x)=−∞  lim_(x→−1^+ ) f(x)=+∞  ⇒there is no minimum and no  maxinum for f(x)!

$$\underset{{x}\rightarrow−\mathrm{1}^{−} } {\mathrm{lim}}{f}\left({x}\right)=−\infty \\ $$$$\underset{{x}\rightarrow−\mathrm{1}^{+} } {\mathrm{lim}}{f}\left({x}\right)=+\infty \\ $$$$\Rightarrow{there}\:{is}\:{no}\:{minimum}\:{and}\:{no} \\ $$$${maxinum}\:{for}\:{f}\left({x}\right)! \\ $$

Commented by benjo_mathlover last updated on 11/Mar/21

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