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Question

Let f(x)={sgn(x),x=0ax2,x0, then which of the following(s) is(are) correct

A
A point of minima exists at x=0, if a<0
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B
A point of minima exists at x=0, if a>0
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C
A point of maxima exists at x=0, if a<0
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D
A point of maxima exists at x=0, if a>0
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Solution

The correct option is C A point of maxima exists at x=0, if a<0
Given : f(x)={0,x=0ax2,x0, as sgn(x)=0 at x=0
Now, f(0)=0,f(0+h)=f(0h)=ah2,h0+

for point of minima at x=0:f(0h)>f(0)<f(0+h)
ah2>0
a>0, as h0+

for point of maxima at x=0:f(0h)<f(0)>f(0+h)
ah2<0
a<0, as h0+

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