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Question

The first derivative of a continuous function $g (x)$ is $g^{'} (x) = 2 x {(x - 2)}^{2}$ . Find the second derivative of $g (x)$ and sketch the general shape of its graph.

Accepted Answer

$g^{'}$ $^{'} (x) = 2 (x - 2) (3 x - 2)$

Graph of a curve with critical points at x=0, x=2/3, and x=2, showing changes in concavity and slope.

Answer

$g^{'}$ $^{'} (x) = 2 (x - 2) (3 x - 2)$

Graph of a curve with critical points at x=0, x=2/3, and x=2, showing changes in concavity and slope.

Answer

$g^{'}$ $^{'} (x) = 2 (x - 2) (3 x - 2)$

Graph of a curve with critical points at x=0, x=2/3, and x=2, showing changes in slope and concavity.

Answer

$g^{'}$ $^{'} (x) = 2 (x - 2) (3 x - 2)$

Graph of a curve with critical points at x=0, x=2/3, and x=2, showing changes in slope and concavity.

The first derivative of a continuous function g(x)g\left(x\right) is g′(x)=2x(x−2)2g^{\prime}\left(x\right)=2x\left(x-2\right)^2. Find the second derivative of g(x)g\left(x\right) and sketch the general shape of its graph.

The first derivative of a continuous function $g (x)$ is $g^{'} (x) = 2 x {(x - 2)}^{2}$ . Find the second derivative of $g (x)$ and sketch the general shape of its graph.