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MHT CET20255 May 2025Evening ShiftMathematicsApplication of DerivativesActual

The minimum value of the slope of the tangent to curve y =x^3-3 x^2+2 x+93 is

Options

  1. A1
  2. B-1
  3. C2
  4. D-2

Correct answer

B. -1

Step-by-step solution

The slope of the tangent to the curve y = x^3 - 3x^2 + 2x + 93 is given by the derivative m(x) = dy dx = 3x^2 - 6x + 2 . Since m(x) is a quadratic with a positive leading coefficient, it attains a minimum at its vertex. The vertex occurs at x = - b 2a = - -6 2 3 = 1 . Evaluating the slope at this point gives m(1) = 3(1)^2 - 6(1) + 2 = -1 . The minimum slope is -1 .

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