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AP EAMCET20225 Jul 2022Morning ShiftMathematicsApplication of DerivativesActual

y=x^3-a x^2+48 x+7 is an increasing function for all real values of x , then a lies in the interval

Options

  1. A(-14,14)
  2. B(-12,12)
  3. C(-16,16)
  4. D(-21,-21)

Correct answer

B. (-12,12)

Step-by-step solution

Given, equation y=x^3-a x^2+48 x+7 Differentiating the above equation with respect to the variable x , we have d y d x =3 x^2-2 a x+48 Thus, above function is a quadratic function. So, D < 0 . In y^ =3 x^2-2 a x+48, A=3, B=-2 a and c=48 D < 0 aligned & (-2 a)^2-4 3 48 < 0 4 a^2-4 3 48 < 0 & 4 (a^2-144 ) < 0 a^2-(12)^2 < 0 & (a-12)(a+12) < 0 & a (-12,12) aligned

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