5. Graphical Applications of Derivatives
Concavity
Practice this topic
- Multiple Choice
For the following graph, find the open intervals for which the function is concave up or concave down. Identify any inflection points.
- Multiple Choice
For the following graph, find the open intervals for which the function is concave up or concave down. Identify any inflection points.
- Multiple Choice
For the following graph, find the open intervals for which the function is concave up or concave down. Identify any inflection points.
- Multiple Choice
The graph of is shown below. Use the graph to determine the intervals for which is concave up or concave down and the location of any inflection points.
- Textbook Question
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?
- Textbook Question
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
- Textbook Question
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
- Textbook Question
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]