5. Graphical Applications of Derivatives

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?

Locating extrema Consider the graph of a function ƒ on the interval [-3, 3]. <IMAGE>

e. On what intervals (approximately) is f concave up?

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

f(x) = ³√(x - 4)

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

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