A function $\mathrm{f}$ is such that $\mathrm{f}'(x) = (x-3)^3$. Find $\mathrm{f}''(x)$.

Question

A function $\mathrm{f}$ is such that $\mathrm{f}'(x) = (x-3)^3$. Find $\mathrm{f}''(x)$. Find $\mathrm{f}'(3)$ and $\mathrm{f}''(3)$. Explain with working, whether the point $P$ on the graph with $x$-coordinate $3$ is a point of inflexion.

Accepted Answer

(a) $\mathrm f''(x)=3(x-3)^2$ (b) $\mathrm f'(3)=0$, $\mathrm f''(3)=0$ (c) $P$ is not a point of inflexion; it is a minimum point.

Applications of Differentiation - Concavity of Graphs

Applications of Differentiation - Concavity of Graphs

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