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AP EAMCET2005MathematicsApplication of Derivatives

Observe the following statements A : f(x)=2 x^3-9 x^2+12 x-3 is increasing outside the interval (1,2) R : f^ (x) < 0 for x (1,2) . Then, which of the following is true?

Options

  1. ABoth A and R are true, and R is not the correct reason for A
  2. BBoth A and R are true, and R is the correct reason for A
  3. CA is true but R is false
  4. DA is false but R is true

Correct answer

A. Both A and R are true, and R is not the correct reason for A

Step-by-step solution

Statement A For increasing function, f^ (x)>0 array lcrl & & & 6 (x^2-3 x+2 )>0 & & 6(x-2)(x-1)>0 & & x 2 array f(x) is increasing outside the interval (1,2) , therefore it is true statement. From Eq. (ii) f^ (x)=6 x^2-18 x+12 for decreasing array lcc & & f^ (x) 1 and x < 2 & f(x) is decreasing in (1,2) . array A and R are both true, but R is not the correct reason.

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