Question
Mathematics Question on Functions
If f(x)=x3−x2f′(1)+xf′′(2)−f′′′(3),x∈R, then
A
2f(0)−f(1)+f(3)=f(2)
B
f(3)−f(2)=f(1)
C
3f(1)+f(2)=f(3)
D
f(1)+f(2)+f(3)=f(0)
Answer
2f(0)−f(1)+f(3)=f(2)
Explanation
Solution
The correct answer is (A) : 2f(0)−f(1)+f(3)=f(2)
f(x)=x3−x2f′(1)+xf′′(2)−f′′′(3),x∈R
Let f′(1)=a,f′′(2)=b,f′′′(3)=c
f(x)=x3−ax2+bx−c
f′(x)=3x2−2ax+b
f′′(x)=6x−2a
f′′′(x)=6
c=6,a=3,b=6
f(x)=x3−3x2+6x−6
f(1)=−2,f(2)=2,f(3)=12,f(0)=−6
2f(0)−f(1)+f(3)=2=f(2)