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AP EAMCET202315 May 2023Morning ShiftMathematicsApplication of DerivativesActual

If the tangent drawn to the curve y=x^3-a x^2+x+1 at each point x R , is inclined at an acute angle with the positive direction of X - axis, then the set of all possible values of ' a ' is

Options

  1. AR -(- 3 , 3 )
  2. B[-3,3]
  3. CR
  4. D(- 3 , 3 )

Correct answer

D. (- 3 , 3 )

Step-by-step solution

Given y=x^3-a x^2+x+1 d y d x =3 x^2-2 a x+1 Since is an acute angle. Hence >0 3 x^2-2 a x+1>0 Which is true off A>0 and D 0 & D < 0 & B^2-4 A C < 0 & (2 a)^2-4(3)(1) < 0 & (a- 3 )(a+ 3 ) < 0 & a (- 3 , 3 ) aligned

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