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Question Number 79472 by jagoll last updated on 25/Jan/20

$$\mathrm{what}\mathrm{the}\mathrm{minimum}\mathrm{value}\mathrm{of}$$$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{{\mathrm{x}}^2+2\mathrm{x}+5}+\sqrt{{\mathrm{x}}^2-14\mathrm{x}+65}$$

Commented by john santu last updated on 25/Jan/20

$$yessir.hahathismethodnot$$$$valid$$

Commented by mr W last updated on 25/Jan/20

$$f=a+bwitha,b>0$$$$‘‘f_{min}occurswhena=b^{″}isvalidonlyif$$$$aandbareindependentfromeach$$$$other.$$$$ifaandbaredependentfromeach$$$$other,suchasinourcase,f_{min}occurs$$$$notalwayswhena=b.\frac{df}{dx}=\frac{da}{dx}+\frac{db}{dx}=0$$$${doesn}^{\prime }tautomaticallyleadtoa=b.$$

Commented by jagoll last updated on 25/Jan/20

Commented by jagoll last updated on 25/Jan/20

$$\mathrm{the}\mathrm{graph}{\mathrm{f}}_{\min }\mathrm{near}\mathrm{to}10\mathrm{sir}$$

Commented by jagoll last updated on 25/Jan/20

$$\underset{x\to 1}{\lim }\mathrm{f}\left(\mathrm{x}\right)=\sqrt{8}+\sqrt{52}=2\sqrt{2}+2\sqrt{13}$$$$=10.039$$

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