- #1
MPC11
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Homework Statement
show that g(x)= x|x| has an inflection point at (0;0) and g'' (0) Does not exist
Does g(x) = x|x| have an inflection point at (0;0) and g''(0) does not exist?
- Thread starter MPC11
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SUMMARY
The function g(x) = x|x| exhibits an inflection point at (0,0), as confirmed by analyzing its behavior around this point. The second derivative g''(0) does not exist due to the discontinuity in the first derivative at x = 0. This conclusion is drawn from the definitions of inflection points and the properties of piecewise functions. The discussion emphasizes the importance of understanding these definitions to solve similar problems effectively.
PREREQUISITES- Understanding of piecewise functions
- Knowledge of derivatives and their continuity
- Familiarity with the concept of inflection points
- Basic calculus, specifically second derivatives
- Study the properties of piecewise functions in calculus
- Learn about the criteria for identifying inflection points
- Explore the concept of continuity and differentiability of functions
- Review examples of functions with discontinuous derivatives
Students studying calculus, particularly those focusing on derivatives and inflection points, as well as educators looking for examples to illustrate these concepts.
show that g(x)= x|x| has an inflection point at (0;0) and g'' (0) Does not exist
- #2
epenguin
Science Advisor
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I can see what they mean. Can you?
Having seen what they mean I can afford to treat this problem with the contempt it deserves.
But you can't.
So what you will have to do is look up the definitions.
Having seen what they mean I can afford to treat this problem with the contempt it deserves.
But you can't.
So what you will have to do is look up the definitions.
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