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SharedClassNotes / Math3b-19-02-R.sagewsOpen in CoCalc

Finding Extrema using the First Derivative Test

Find and classify the stationary points of the following curves y=f(x)y=f(x)

  • y=3x230min:(0,30)y=3x^2 - 30 \qquad \qquad \color{red}{\text{min:} (0,30)}
  • y=2x33x2max:(0,0),min:(1,1)y=2x^3 - 3x^2 \qquad \qquad \color{red}{\text{max:} (0,0), \text{min:} (1, -1)}
  • y=x33x245xmax:(3,81),min:(5,175)y=x^3 - 3x^2 - 45x \qquad \qquad \color{red}{\text{max:} (-3,81), \text{min:} (5, 175)}
  • y=x36x2+9x+1max:(1,5),min:(3,1)y=x^3- 6x^2 + 9x + 1 \qquad \qquad \color{red}{\text{max:} (1,5), \text{min:} (3, 1)}
  • y=x33x21min:(2,5),max:(0,1)y= -x^3 - 3x^2 - 1 \qquad \qquad \color{red}{\text{min:} (-2,-5), \text{max:} (0, -1)}
  • y=27xx3min:(3,53),max:(3,54)y=27x - x^3 \qquad \qquad \color{red}{\text{min:} (-3,53), \text{max:} (3, 54)}
  • y=x42x2+3min:(1,2),max:(0,3),min:(1,2)y = x^4 - 2x^2 + 3 \qquad \qquad \color{red}{\text{min:} (-1,2), \text{max:} (0, 3), \text{min:} (1, 2)}
  • y=x35x2+7x5max:(1,2),min:(7/3,86/27)y=x^3 - 5x^2 + 7x - 5 \qquad \qquad \color{red}{\text{max:} (1,-2), \text{min:} (7/3, -86/27)}

You can find solutions using: SageMathCell