- #1
angela107
- 35
- 2
- Homework Statement
- Given ##f(x)=3x^5-5x^3##, find all critical points and identify any local
max/min point.
- Relevant Equations
- n/a
Is my work right?
Given ##f(x)=3x^5-5x^3##, find all critical points.
- Thread starter angela107
- Start date
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- Tags
- Critical points Points
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SUMMARY
The discussion focuses on finding critical points for the function f(x) = 3x^5 - 5x^3. Participants emphasize the importance of verifying the factorization of the second derivative, y'', to ensure accurate identification of critical points. It is confirmed that the first derivative exists for all x, indicating that there are no points where the derivative is undefined. Therefore, the analysis primarily revolves around the critical points derived from the first derivative.
PREREQUISITES- Understanding of calculus concepts, specifically derivatives and critical points.
- Familiarity with polynomial functions and their properties.
- Knowledge of factorization techniques for derivatives.
- Ability to analyze the behavior of functions based on their derivatives.
- Review the process of finding critical points for polynomial functions.
- Learn about the significance of the second derivative test in determining concavity.
- Study the implications of points where the derivative does not exist.
- Explore advanced factorization techniques for higher-order derivatives.
Students and professionals in mathematics, particularly those studying calculus, as well as educators looking for examples of critical point analysis in polynomial functions.
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