Find the coordinates of the stationary points on the curve $y=2x^3+3x^2+x-5$. Determine the nature

Question

Find the coordinates of the stationary points on the curve $y=2x^3+3x^2+x-5$. Determine the nature of each point by using the second derivative test. Hence, sketch the curve.

Accepted Answer

Maximum point $\left(\frac{-3-\sqrt{3}}{6},-5+\frac{\sqrt{3}}{18}\right)\approx(-0.789,-4.90)$; minimum point $\left(\frac{-3+\sqrt{3}}{6},-5-\frac{\sqrt{3}}{18}\right)\approx(-0.211,-5.10)$. The sketch crosses the axes at $(0,-5)$ and $(0.919,0)$ approximately.

Applications of Differentiation - Stationary Points and Their Nature

Applications of Differentiation - Stationary Points and Their Nature

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