JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \( f(x)=x^{3}+x^{2}f^{\prime}(1)+2x~f^{\prime\prime}(2)+f^{\prime\prime\prime}(3), x\in R. \) Then the value of \(f^{\prime}(5)\) is :
- A \( \frac{62}{5} \)
- B \( \frac{657}{5} \)
- C \( \frac{2}{5} \)
- D \( \frac{117}{5} \)
Answer & Solution
Correct Answer
(D) \( \frac{117}{5} \)
Step-by-step Solution
Detailed explanation
\( f^{\prime}(x)=3x^{2}+2xf^{\prime}(1)+2f^{\prime}(2) \) \( f^{\prime}(x)=6x+2f^{\prime}(1) \) \( f^{\prime\prime}(2)=12+2f^{\prime}(1) \) \( \therefore f^{\prime}(x)=3x^{2}+2xf^{\prime}(1)+2(12+2f(1)) \) \( f^{\prime}(x)=3x^{2}+2(x+2)f(1)+24 \) Putting, \( x=1 \)…
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