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B
f(x) is strictly decreasing on the left of 0
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C
f′(x) is strictly increasing on the left of 0
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D
f(x) is strictly increasing on the right of 0
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Solution
The correct option is Af(x) has a maximum at x=0 f(x)=⎧⎪⎨⎪⎩x2+2,x<02x=0x+2x>0 Here f(0)=2 limx→0−f(x)=2 limx→0+f(x)=2 f′(x)=2x,x<0 ∴f′(x)<0 for x<0 ∴f(x) is decreasing on the left of 0. Hence at x=0, there is no maximum. f"(x)=2,x<0 ∴f"(x)>0,x<0 ∴f′(x) is increasing on the left of 0. f′(x)=1,x>0 ∴f(x) is strictly increasing on the right of 0.