Given the following graph, state the intervals concave down

Thread starter angela107
Start date May 28, 2020
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Concave Graph intervals State

In summary, a concave down interval is a section of a graph where the curve is curving downwards, indicating a decreasing slope. It can be identified by looking for a concave shape on the graph. This interval indicates that the slope of the curve is decreasing at an increasing rate. It does not necessarily have to be negative, as the values on the y-axis can vary. Concave down intervals are related to the second derivative of a function, as the second derivative measures the rate of change of the slope, which determines the concavity of the curve.

May 28, 2020

angela107

Homework Statement: Is this answer correct?

Relevant Equations: n/a

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May 28, 2020

LuccaP4

I think is correct. The second derivative in ##x>0## equals ##0## and in ##-6<x<-2## the function is concave up.
## x=-2 ## would be the point of inflection.

1. What does it mean for a graph to be concave down?

When a graph is concave down, it means that the shape of the curve is facing downwards, resembling a frown. This indicates that the function is decreasing at an increasing rate.

2. How can you determine the intervals where a graph is concave down?

To determine the intervals where a graph is concave down, you need to look for points on the graph where the slope of the curve is decreasing. This means that the second derivative of the function is negative in those intervals.

3. What is the significance of knowing the intervals where a graph is concave down?

Knowing the intervals where a graph is concave down can help in understanding the behavior of the function. It can also be used to identify the maximum points on the graph, as the concavity changes from down to up at these points.

4. Can a graph be concave down at multiple intervals?

Yes, a graph can be concave down at multiple intervals. This means that the function is decreasing at an increasing rate in those intervals.

5. How can you use the information about concavity to analyze a graph?

The information about concavity can help in analyzing the behavior of the function. It can be used to identify the maximum and minimum points on the graph, as well as the points of inflection. It can also help in determining the direction of the graph at different points.