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Question

The third derivative of a function f(x) vanishes for all x. lf f(0)=1,f′(1)=2, and f′(2)= -1 then f(x)=

A
x3+3x+2
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B
x23x+12
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C
x2+3x12
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D
3x2+10x+22
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Solution

The correct option is D 3x2+10x+22

Letf(x)=ax2+bx+c(as f(x)=0)
f(0)=c , c=1.....(1)
f(x)=2ax+b
f′′(1)=2a+b=2
f′′(2)=4a+b=1

a=32,b=5,c=1


f(x)=3x2+10x+22


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