WBJEE · Maths · Application of Derivatives
If the function \(f(x)=2 x^{3}-9 a x^{2}+12 a^{2} x+1[a>0]\) attains its maximum and minimum at \(p\) and \(q\) respectively such that \(\mathrm{p}^{2}=\mathrm{q}\), then \(\mathrm{a}\) is equal to
- A 2
- B \(\frac{1}{2}\)
- C \(\frac{1}{4}\)
- D 3
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
Hint: \(f^{\prime}(x)=6 x^{2}-18 a x+12 a^{2} \Rightarrow f^{\prime \prime}(x)=12 x-18 a \Rightarrow f^{\prime}(x)=0 \Rightarrow x=a, 2 a\) \(f^{\prime}(a) 0 ; q=2 a\) (minimum) \(a^{2}=2 a ; a(a-2)=0, \quad a=2\)
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