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NDA2021MathematicsApplication of DerivativesActual

The curve y=-x^3+3 x^2+2 x-27 has the maximum slope at

Options

  1. Ax=-1
  2. Bx=0
  3. Cx=1
  4. Dx=2

Correct answer

C. x=1

Step-by-step solution

Curve y=-x^3+3 x^2+2 x-27 Slope = d y d x =-3 x^2+6 x+2 Again, d^2 y d x^2 =-6 x+6 For maximum slope d^2 y d x^2 =0 6(-x+1)=0 x=1 Hence, the curve has maximum slope at x=1 .

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