Find the coordinates of the stationary points on the curve $y=12x^3+3x^2-6x+1$. Determine the natu

Question

Find the coordinates of the stationary points on the curve $y=12x^3+3x^2-6x+1$. Determine the nature of each point by using the first derivative test. Hence, sketch the curve.

Accepted Answer

Maximum point $\left(-\frac{1}{2},\frac{13}{4}\right)$; minimum point $\left(\frac{1}{3},-\frac{2}{9}\right)$. The sketch crosses the $y$-axis at $(0,1)$ and the $x$-axis at $x\approx-0.905,\ 0.205,\ 0.450$.

First Derivative Test

First Derivative Test

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