Let f(x) be a polynomial of degree 3 such that `f(3)=1, f'(3)=-1, f''(3)=0, and f'''(3)=12.` Then the value of f'(1) is

Options

A. 12
B. 23
C. -13
D. none of these

Answer

B

Explanation

Let `f(x)=a(x-3)^(3)+(x-3)^(2)+c(x-3)+d` be the given polynomial. Then,
`{:(" "f(3)=1,,impliesd=1),(" "f'(3)=-1,,impliesc=-1),(" "f''(3)=0,,impliesb=0),("and"","f'''(3)=12,,implies6a=12impliesa=2):}`
`:." "f(x)=2(x-3)^(3)-(x-3)+1`
`implies" "f'(x)=6(x-3)^(2)-1" "impliesf'(1)=23`