JEE Mains · Maths · STD 12 - 6. Application of derivatives
In an \(A.P.\), the sixth terms \(a_6=2\). If the \(a_1 a_4 a_5\) is the greatest, then the common difference of the \(A.P.,\) is equal to
- A \(\frac{3}{2}\)
- B \(\frac{3}{2}\)
- C \(\frac{2}{3}\)
- D \(\frac{5}{8}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\( a_6=2 \Rightarrow a+5 d=2 \) \(a_1 a_4 a_5=a(a+3 d)(a+4 d)\) \(=(2-5 d)(2-2 d)(2-d) \) \(f(d)=8-32 d+34 d^2-20 d+30 d^2-10 d^3\) \(f^{\prime}(d)=-2(5 d-8)(3 d-2) \) \(\frac{-1}{2 / 3}+\frac{1}{8 / 5}\) \(d=\frac{8}{5}\)
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