5. Graphical Applications of Derivatives

Determine the intervals for which the function is concave up or concave down. State the inflection points.

$f(x)=2x(x+9)^2$

Suppose the graph of $y=f\left(x\right)$ is shown above. Which of the following best describes the graph of $y=f^{″}\left(x\right)$?

At the point with x-coordinate $-2$, is the graph of $g\left(x\right)=4x^3+9x^2+7x+3$ concave up or concave down?

For the following graph, find the open intervals for which the function is concave up or concave down. Identify any inflection points.

For the following graph, find the open intervals for which the function is concave up or concave down. Identify any inflection points.

Determine the intervals for which the function is concave up or concave down. State the inflection points.

$f(x)=\(\frac{7}{2x-9}\)$

The graph of $f^{\(\prime\)}\(\left\)(x\(\right\))$is shown below. Use the graph to determine the intervals for which $f\(\left\)(x\(\right\))$is concave up or concave down and the location of any inflection points.

The graph of $f''(x)$ is shown below. Use the graph to determine the intervals for which $f\(\left\)(x\(\right\))$is concave up or concave down and the location of any inflection points.

For the following graph, find the open intervals for which the function is concave up or concave down. Identify any inflection points.

Determine the intervals for which the function is concave up or concave down. State the inflection points. 

$f(x)=2\(\sin\) x+3x$; $0$ < $x$ < $2\(\pi\)$