1.

Let f:RtoR be a function such that f(x)=x^(3)+x^(2)f'(1)+xf"(2)+f"(3),xinR. Then f(2) equals:

Answer»

30
8
2
`-4`

SOLUTION :`f(x)=x^(3)+x^(2)f'(1)+XF"(2)+f"'(3)`
f"(3)=6
`f'(x)=3x^(2)+2xf'(1)+f"(2)`
`f'(1)=3+2f'(1)+f"(2)`
`f'(1)+f"(2)+3=0` …(i)
`f"(x)=6x+2f'(1)`
f"(2)=12+2f'(1) …(ii)
Substitute in (i)
`f'(1)+12+2f'(1)+3=0`
`rArrf'(1)=-5F"(2)=2`
`f(x)=x^(3)-5X^(2)+2x+6`
f(2)=2


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