JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f(x)\) be a polynomial function such that \(f(x)+f^{\prime}(x)+f^{\prime \prime}(x)=x^{5}+64\). Then, the value of \(\lim _{x \rightarrow 1} \frac{f(x)}{x-1}\)
- A \(-15\)
- B \(-60\)
- C \(60\)
- D \(15\)
Answer & Solution
Correct Answer
(A) \(-15\)
Step-by-step Solution
Detailed explanation
\(\operatorname{Lt}_{x \rightarrow 1} \frac{f(x)}{x-1}=f^{\prime}(1)(\) and \(f(1)=0)\) \(f(x)+f^{\prime}(x)+t^{\prime \prime}(x)=x^{5}+64\) \(f^{\prime}(x)+f^{\prime \prime}(x)+f^{\prime \prime \prime}(x)=5 x^{4}\)…
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