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**Showing the inequality holds for an interval (???)**

## Homework Statement

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]

## Homework Equations

## 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.