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Question

Consider the graph of a twice-differentiable function $f (x)$ . Determine whether $f^{'} (x)$ and $f^{'}$ $^{'} (x)$ are positive, negative, or zero at point $A$ .

Graph of a red curve with point A marked, illustrating concavity and derivative behavior on a grid.

Accepted Answer

$f^{'} (x)$ is zero and $f^{'}$ $^{'} (x)$ is positive

Answer

$f^{'} (x)$ is positive and $f^{'}$ $^{'} (x)$ is zero

Answer

$f^{'} (x)$ is positive and $f^{'}$ $^{'} (x)$ is negative

Answer

$f^{'} (x)$ and $f^{'}$ $^{'} (x)$ are both zero

Consider the graph of a twice-differentiable function f(x)f\(\left\)(x\(\right\)). Determine whether f′(x)f^{\(\prime\)}\(\left\)(x\(\right\)) and f′f^{\(\prime\)}′(x)^{\(\prime\)}\(\left\)(x\(\right\)) are positive, negative, or zero at point AA.

Consider the graph of a twice-differentiable function $f (x)$ . Determine whether $f^{'} (x)$ and $f^{'}$ $^{'} (x)$ are positive, negative, or zero at point $A$ .