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The function f(x)=2|x|+|x+2|=||x|2|-2|x|...

The function `f(x)=2|x|+|x+2|=||x|2|-2|x||` has a local minimum or a local maximum at `x=` `-2` (b) `-2/3` (c) 2 (d) `2/3`

A

-2

B

`-2//3`

C

2

D

`2//3`

Text Solution

Verified by Experts

The correct Answer is:
1,2
As `f(x)+g(x)-|f(x)-f(x)|(2)=Min (f(x),g(x)`
`rarr (2|x|+|x+2|-||x+2|-2x||)/(2)=min(|2x|,|+2|)`

From the figure shown points of local minima/maxima are
`x=-2,2//3,0`
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