- #1
angela107
- 35
- 2
- Homework Statement
- Is this answer correct?
- Relevant Equations
- n/a
Given the following graph, state the intervals concave down
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SUMMARY
The discussion centers on identifying the intervals where a function is concave down based on its second derivative. It is established that for ##x > 0##, the second derivative equals ##0##, indicating a change in concavity. The interval ##-6 < x < -2## is confirmed to be concave up, with ##x = -2## identified as the point of inflection where the concavity changes.
PREREQUISITES- Understanding of second derivatives in calculus
- Knowledge of concavity and points of inflection
- Familiarity with interval notation
- Basic graph interpretation skills
- Study the concept of second derivatives in calculus
- Learn how to determine concavity from a function's graph
- Explore the relationship between inflection points and concavity
- Practice identifying concave intervals using various functions
Students studying calculus, educators teaching mathematical concepts, and anyone interested in understanding the behavior of functions through their derivatives.
- #2
LuccaP4
- 24
- 9
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.
## x=-2 ## would be the point of inflection.
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