5. Graphical Applications of Derivatives

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.

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

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.

Concavity of parabolas Consider the general parabola described by the function f(x) = ax² + bx + c. For what values of a, b, and c is f concave up? For what values of a, b, and c is f concave down?

Concavity Determine the intervals on which the following functions are concave up or concave down. Identify any inflection points.

f(x) = 2x⁴ + 8x³ + 12x² - x - 2

Concavity Determine the intervals on which the following functions are concave up or concave down. Identify any inflection points.

g(t) = 3t⁵ - 30t⁴ + 80t³ + 100

Concavity Determine the intervals on which the following functions are concave up or concave down. Identify any inflection points.

h(t) = 2 + cos 2t on [0,π]