JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(f(x)=x^3-x^2 f^{\prime}(1)+x f^{\prime \prime}(2)-f^{\prime \prime \prime}(3), x \in R\), then
- A \(3 f(1)+f(2)=f(3)\)
- B \(f(3)-f(2)=f(1)\)
- C \(2 f (0)- f (1)+ f (3)= f (2)\)
- D \(f(1)+f(2)+f(3)=f(0)\)
Answer & Solution
Correct Answer
(C) \(2 f (0)- f (1)+ f (3)= f (2)\)
Step-by-step Solution
Detailed explanation
\(f(x)=x^3-x^2 f^{\prime}(1)+x f^{\prime \prime}(2)-f^{\prime \prime \prime}(3), x \in R\) Let \(f^{\prime}(1)=a, f^{\prime \prime}(2)=b, f^{\prime \prime \prime}(3)=c\) \(f(x)=x^3-a^2+b x-c\) \(f^{\prime}(x)=3 x^2-2 a x+b\) \(f^{\prime \prime}(x)=6 x-2 a\)…
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