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Finding Extrema using the First Derivative Test

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

• $y=3x^2 - 30 \qquad \qquad \color{red}{\text{min:} (0,30)}$
• $y=2x^3 - 3x^2 \qquad \qquad \color{red}{\text{max:} (0,0), \text{min:} (1, -1)}$
• $y=x^3 - 3x^2 - 45x \qquad \qquad \color{red}{\text{max:} (-3,81), \text{min:} (5, 175)}$
• $y=x^3- 6x^2 + 9x + 1 \qquad \qquad \color{red}{\text{max:} (1,5), \text{min:} (3, 1)}$
• $y= -x^3 - 3x^2 - 1 \qquad \qquad \color{red}{\text{min:} (-2,-5), \text{max:} (0, -1)}$
• $y=27x - x^3 \qquad \qquad \color{red}{\text{min:} (-3,53), \text{max:} (3, 54)}$
• $y = x^4 - 2x^2 + 3 \qquad \qquad \color{red}{\text{min:} (-1,2), \text{max:} (0, 3), \text{min:} (1, 2)}$
• $y=x^3 - 5x^2 + 7x - 5 \qquad \qquad \color{red}{\text{max:} (1,-2), \text{min:} (7/3, -86/27)}$

You can find solutions using: SageMathCell