If f(x)=∣∣|x|2−2|x|−3∣∣, then f(x) is not differentiable at x equal to
A
−1,0,1
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B
1,2
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C
−3,−1,0,1,3
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D
−3,0,3
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Solution
The correct option is D−3,0,3 f(x)=∣∣|x|2−2|x|−3∣∣
The graph of the function f(x) is obtained as:
From graph of ||x|2−2|x|−3| it is evident that at x=−3,0,3 it has sharp edges. ∴ At x=0,3,−3,f(x) is not differentiable.