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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

Paragraph: Let f( x )= x ^3-3 x +1, x R and a , b , c are roots of f( x )=0, P ( , f( )) is point of local minima Q ( , f( )) is point of local maxima and R ( , f( )) is point of inflection in the graph of y =f( x ) . On the basis of above information answer the following : Question: Number of distinct real solutions of f(f( x ))=0 are -

Options

  1. A3
  2. B5
  3. C7
  4. D9

Correct answer

C. 7

Step-by-step solution

aligned & f^ (x)=3 (x^2-1 ) & f(0)=1 & f(1)=-1 & f(-1)=3 & f(f(x))=0 aligned aligned & f^3( x )-3 f( x )+1=0 f( x )= , , & f( x )= aligned exactly one solution as (-1,-2)f(x)= exactly three distinct solutions as (0,1)f( x )= exactly three distinct solutions as (1,2) so total seven solutions.

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