A curve has the equation $y = x^3 + 3x^2 - 9x + p$, where $p$ is a constant. Find, in terms

Question

A curve has the equation $y = x^3 + 3x^2 - 9x + p$, where $p$ is a constant. Find, in terms of $p$, the coordinates of the stationary point(s) on the curve. Determine the nature of the stationary point(s). Hence find the possible value(s) of $p$, such that the curve has a stationary point on the $x$-axis.

Accepted Answer

(i) $(-3,p+27)$, $(1,p-5)$ (ii) Maximum at $(-3,p+27)$; minimum at $(1,p-5)$ (iii) $p=-27$ or $p=5$

Applications of Differentiation - Stationary Points and Their Nature

Applications of Differentiation - Stationary Points and Their Nature

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