CPM Homework Help : APCALC Problem 11-75

Multiple Choice: The graph of $y = f(x)$ is shown at right. $f$ is twice differentiable. Examine the graph and decide which statement below is true.

$f(2) < f^\prime(2) < f^{\prime\prime}(2)$
$f(2) < f^{\prime\prime}(2) < f ^\prime(2)$
$f^\prime(2) < f(2) < f^{\prime\prime}(2)$
$f^{\prime\prime}(2) < f(2) < f ^\prime(2)$
$f^{\prime\prime}(2) < f^\prime(2) < f(2)$

Increasing curve, coming from bottom, right of y axis, changing from concave down to concave up at the point (2, comma negative 5), continuing up & passing through the point (3.5, comma 0).

Steps:

Approximate:
$f\left(2\right)$
$f ′\left(2\right)$
$f ″\left(2\right)$

Partial answer:

$f(2) < 0$
$f ′(2) > 0$
$f ″(2) ≈ 0$