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MHT CET2007MathematicsApplication of Derivatives

If the function f(x)=2 x³-9 a x²+12 a² x+1 attains its maximum and minimum at p and q respectively such that p²=q , then a equals

Options

  1. A0
  2. B1
  3. C2
  4. DNone of these

Correct answer

C. 2

Step-by-step solution

Given, f(x)=2 x³-9 a x²+12 a² x+1 attains maximum and minimum at p and q respectively. f^ (p)=0, f^ (q)=0 Now, array c f^ (p) 0 f^ (p)=0 array and array r f^ (q)=0 6 p²-18 a p+12 a²=0 6 q²-18 a q+12 a²=0 array and array ll & p²-3 a p+2 a²=0 and & q²-3 a q+2 a²=0 array p=a, 2 a, q=a, 2 a array lrl & p=a, 2 a, q=a, Now, & f^ (p) 0 12 q-18 a>0 q> 3 2 a From Eqs. (i), (ii) and (iii), we get aligned p &=a, q=2 a Now, p² &=q aligned array lc & a²=2 a & a=0,2 array But for a=0, f(x)=2 x³+1 which does not attains a maximum

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