TS EAMCET · Maths · Application of Derivatives
The function \(f(x)=2 x^3-9 a x^2+12 a^2 x+1\) where \(\mathrm{a}>0\) attains its local maximum and local minimum at \(p\) and \(q\) respectively. If \(p^2=q\) then \(a=\)
- A 1
- B 2
- C 3
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
\(f'(x) = 6x^2 - 18ax + 12a^2\) \(6x^2 - 18ax + 12a^2 = 0\) \(x^2 - 3ax + 2a^2 = 0\) \((x - a)(x - 2a) = 0\) \(x = a\) or \(x = 2a\) \(f''(x) = 12x - 18a\) \(f''(a) = 12a - 18a = -6a \(f''(2a) = 12(2a) - 18a = 6a > 0 \implies q = 2a\) \(p^2 = q\) \(a^2 = 2a\)…
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