JEE Mains · Maths · STD 12 - 6. Application of derivatives
If \(a_n\) is the greatest term in the sequence \(a _{ n }=\frac{ n ^3}{ n ^4+147}, n =1,2,3 \ldots \ldots\). , then \(\alpha\) is equal to \(..........\).
- A \(4\)
- B \(5\)
- C \(3\)
- D \(6\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{x^3}{x^4+147}\) \(f^{\prime}(x)=\frac{\left(x^4+147\right) 3 x^2-x^3\left(4 x^3\right)}{\left(x^4+147\right)^2}\) \(=\frac{3 x^6+147 \times 3 x^2-4 x^6}{+v e}=x^2\left(44-x^4\right)\) \(f ^{\prime}( x )=0 \text { at } x ^6=147 \times 3 x ^2\)…
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