A curve has equation $y = x^3 + 3x^2 - 9x + p$, where $p$ is a constant. Write down an expr

Question

A curve has equation $y = x^3 + 3x^2 - 9x + p$, where $p$ is a constant. Write down an expression for $\frac{\mathrm{d}y}{\mathrm{d}x}$. Find the $x$-coordinates of the two stationary points on the curve. Hence find the two possible values of $p$ for which the curve has a stationary point on the $x$-axis.

Accepted Answer

(a) $3x^2+6x-9$ (b) $x=-3$ or $x=1$ (c) $p=5$ or $p=-27$

Applications of Differentiation - Stationary Points and Their Nature

Applications of Differentiation - Stationary Points and Their Nature

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