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KCET2021MathematicsApplication of Derivatives

The maximum slope of the curve y=-x³+3 x²+2 x-27 is

Options

  1. A1
  2. B23
  3. C5
  4. D-23

Correct answer

C. 5

Step-by-step solution

y=-x³+3 x²+2 x-27 On differentiating w.r.t. x , we get d y d x =-3 x²+6 x+2 Slope of the curve =-3 x²+6 x+2 Let m=-3 x²+6 x+2 d m d x =-6 x+6 Put d m d x =0 to find the critical points, aligned &-6 x+6 &=0 x &=1 & ( d² m d x² )_ x=1 =-6 < 0 aligned Slope is maximum at x=1 The maximum slope, aligned m_ &=-3(1)²+6(1)+2 &=-3+6+2=5 aligned

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