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BITSAT2014MathematicsApplication of DerivativesActual

The interval in which the function 2 x ³+15 increases less rapidly than the function 9 x²-12 x, is -

Options

  1. A(- , 1)
  2. B(1,2)
  3. C(2, )
  4. DNone of these

Correct answer

B. (1,2)

Step-by-step solution

Let f(x)=2 x³+15 and g(x)=9 x²-12 x then f ^ ( x )=6 x ² x R f ( x ) is increasing function x R Also, g^ (x)>0 18 x-12>0 x> 2 3 Thus, f ( x ) and g ( x ) both increases for x > 2 3 Let F(x)=f(x)-g(x), F^ (x)<0 ( f ( x ) increases less rapidly than the function g ( x )) 6 x ²-18 x +12<0 1< x <2

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