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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2021 · Mathematics · Application of Derivatives

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

The curve y=−x3+3x2+2x−27y=-x^3+3 x^2+2 x-27 has the maximum slope at

Options

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

Correct answer

C. x=1x=1

Step-by-step solution

Curve y=−x3+3x2+2x−27y=-x^3+3 x^2+2 x-27 Slope =dydx=−3x2+6x+2=\frac{d y}{d x}=-3 x^2+6 x+2 Again, d2ydx2=−6x+6\frac{d^2 y}{d x^2}=-6 x+6 For maximum slope d2ydx2=0⇒6(−x+1)=0∴x=1\frac{d^2 y}{d x^2}=0 \Rightarrow 6(-x+1)=0\therefore x=1 Hence, the curve has maximum slope at x=1x=1.
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