(adsbygoogle = window.adsbygoogle || []).push({}); Showing the inequality holds for an interval (???)

1. The problem statement, all variables and given/known data

Hi, my homework question is:

Show that the inequality

[itex]\sqrt{2+x}[/itex]<2+[itex]\frac{x}{4}[/itex] holds [itex]\forall[/itex]x[itex]\in[/itex][-2,0]

2. Relevant equations

3. The attempt at a solution

I tried using IVT or bisection method, but they are just for existence of a root. How can I show it holds for all x in the interval [-2,0]? Would taking the derivative of the function

[itex]\sqrt{2+x}[/itex]-2-[itex]\frac{x}{4}[/itex] lead me anywhere? Like finding maximum or minimum points? Thanks a lot for any help.

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# Homework Help: Showing the inequality holds for an interval (?)

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