1. Tardigrade
  2. Question
  3. Mathematics
  4. Suppose mathrmx1 mathrmx2 are the point of maximum and the point of minimum respectively of the function f(x)=2 x3-9 a x2+12 a2 x+1 respectively, then for the equality x12=x2 to be true the value of 'a' must be

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Q. Suppose $\mathrm{x}_{1} \& \mathrm{x}_{2}$ are the point of maximum and the point of minimum respectively of the function $f(x)=2 x^{3}-9 a x^{2}+12 a^{2} x+1$ respectively, then for the equality $x_{1}^{2}=x_{2}$ to be true the value of 'a' must be

Application of Derivatives

Solution:

$f^{\prime}(x)=6\left(x^2-3 a x+2 a^2\right)=6(x-2 a)(x-a)=0 \Rightarrow x=2 a \text { or } a $
$f^{\prime \prime}(x)=6(2 x-3 a)$

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