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f(x)=|x^2-3|x|+2|dot Then which of the f...

`f(x)=|x^2-3|x|+2|dot` Then which of the following is/are true

A

`f'(x)=2x-3" for " x in (0,1) cup (2, oo)`

B

`f'(x)=2x +3 for x in (-oo,-2) cup (-1,0)`

C

`f'(x)=-2x-3" for "x in (-2,-1)`

D

None of these

Text Solution

Verified by Experts

`f(x)=|x^(2)-3x+2|, xge0`
`={{:(|x^(2)-3x+2|",",xge0),(|x^(2)+3x+2|",",xlt0):}`
`{{:(x^(2)-3x+2,x^(2)-3x+2ge,xge0),(-x^(2)+3x-2, x^(2)-3x+2lt0,xge0),(x^(2)+3x+2,x^(2)+3x+2ge0,xlt0),(-x^(2)-3x-2,x^(2)+3x+2lt0,xlt0):}`
`={{:(x^(2)-3x+2",",x in [0, 1] cup[2, oo]),(-x^(2)+3x-2",",x in (1,2)),(x^(2)+3x+2",", x in (-oo,-2]cup[-1,0]),(-x^(2)-3x+2",", x in (-2,-1)):}`
`"or "f'(x)={{:(2x-3",", x in (0,1) cup (2,oo)),(-2x+3",", x in (1,2)),(2x+3",", x in (-oo,-2)cup(-1,0)),(-2x-3",", x in (-2,-1)):}`
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