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Question

If f(x + y) = f(x) + f(y) + 2xy - 6 for all x,yϵR and f'(0) = 2, then y = f(x) will be


A
straight line
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B
parabola
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C
ellipse
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D
circle
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Solution

The correct option is B parabola
f(x)=limn0f(x+h)f(x+0)h=limn0f(x)+f(h)+2xh6f(x)f(0)+6h=2x+limn0f(0+h)f(0)h=2x+f(0)f(x)=x2+2x+6
So, f(x)=x2+2x+6.

Mathematics

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