It is given that \(\mathrm{f}\,\text{ }'\!\!\text{ }\left( x \right)=\left( x-1 \right)\left( x

Question

It is given that $\mathrm{f}\,\text{ }'\!\!\text{ }\left( x \right)=\left( x-1 \right)\left( x-3 \right){{\left( x-4 \right)}^{2}}$. Find the $x$-coordinate(s) of the stationary points of $\mathrm{f}$ and determine their nature. It is given that $\mathrm{f}\,\text{ }'\!\!\text{ }\!\!'\!\!\text{ }\left( x \right)=\left( x-1 \right)\left( x-3 \right){{\left( x-4 \right)}^{2}}$. Find the $x$-coordinate(s) of the points of inflexion of $\mathrm{f}$ and justify your answer.

Accepted Answer

(a) $x=1$(max), $x=3$ (min), $x=4$ (stationary point of inflexion) (b) $x=1$, $x=3$ (point of inflexion)

Applications of Differentiation - Concavity of Graphs

Applications of Differentiation - Concavity of Graphs