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KVPY2015MathematicsApplication of Derivatives

Let f(x)=a x²-2+ 1 x where is a real constant. The smallest for which f(x) 0 for all x>0 is

Options

  1. A2² 3³
  2. B2³ 3³
  3. C2⁴ 3³
  4. D2⁵ 3³

Correct answer

D. 2⁵ 3³

Step-by-step solution

array ll f(x)= x³-2 x+1 x 0 & x (0, ) x³-2 x+1 0 & x (0, ) Now Let (x)= x³-2 x+1 & array ^ (x)=3 x²-2=0 x= 2 3 So Graph of ( x ) array l ( 2 3 ) 0 2 3 [ 2 3 -2 ]+1 0 array 2 3 [- 4 3 ]+1 0 2 3 3 4 2 3 9 16 = 32 27

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