A curve is such that $\frac{\mathrm{d}^2y}{\mathrm{d}x^2} = 36x^2$. The curve has a turning point

Question

A curve is such that $\frac{\mathrm{d}^2y}{\mathrm{d}x^2} = 36x^2$. The curve has a turning point $(-1, -9)$. Find the equation of the curve. Determine, with working, whether there are any other turning points on the curve.

Accepted Answer

(a) $y=3x^4+12x$ (b) No other turning points

Applications of Differentiation - Stationary Points and Their Nature

Applications of Differentiation - Stationary Points and Their Nature

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