AP EAMCET · Maths · Application of Derivatives
For \(a>0\), if the function \(f(x)=2 x^3-9 a x^2+12 a^2 x+1\) attains its maximum value at \(p\) and minimum value at \(q\) such that \(p^2=q\), then \(a=\)
- A \(\frac{1}{2}\)
- B 1
- C 2
- D 4
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
Given, \(f(x)=2 x^3-9 a x^2+12 a^2 x+1\) has maximum value at \(P\) and minimum value at \(q\). So, \(f^{\prime}(p)=0\) and \(f^{\prime}(q)=0\) Now, \(f^{\prime}(x)=6 x^2-18 a x+12 a^2\) has roots \(p\) and \(q\)…
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