JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(a_1, a_2, a_3, ……\) be and \(A.P\) with \(a_6 = 2.\) Then the common difference of this \(A.P.,\) which maximizes the product \(a_1a_4a_5\) is
- A \(\frac {3}{2}\)
- B \(\frac {8}{5}\)
- C \(\frac {2}{3}\)
- D \(\frac {6}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac {8}{5}\)
Step-by-step Solution
Detailed explanation
Let a is first term and d is common difference then, \(a+5 d=2\) (given) \(\ldots..........(1)\) \(f(d)=(2-5 d)(2-2 d)(2-d)\) \(f^{\prime}(x)=0 \Rightarrow d=\frac{2}{3}, \frac{8}{5}\) \(f^{\prime \prime}(d)<0\) at \(d=\frac{8}{5}\) \(\Rightarrow \mathrm{d}=\frac{8}{5}\)
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