- #1
angela107
- 35
- 2
- Homework Statement
- Given ##f(x) = 3x^5 − 5x^3##, what are the intervals of concave up and concave down?
- Relevant Equations
- n/a
Is this correct?
Solving for intervals of concave up and concave down
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SUMMARY
The discussion focuses on determining the intervals of concavity for the function f(x) = 3x^5 − 5x^3. The correct approach involves finding the second derivative of the function, which is f''(x) = 30x^4 - 30x. The intervals of concave up occur where f''(x) > 0, and concave down where f''(x) < 0. The critical points for concavity are found at x = 0, leading to the conclusion that the function is concave up on the intervals (-∞, -1) and (1, ∞), and concave down on the interval (-1, 1).
PREREQUISITES- Understanding of calculus concepts, specifically derivatives and concavity.
- Familiarity with polynomial functions and their properties.
- Knowledge of how to find critical points and test intervals.
- Ability to compute and interpret second derivatives.
- Learn how to compute the second derivative of polynomial functions.
- Study the relationship between the second derivative and concavity.
- Explore the application of the first and second derivative tests in determining local extrema.
- Investigate the implications of concavity on the graph of a function.
Students studying calculus, educators teaching polynomial functions, and anyone seeking to understand the concepts of concavity and inflection points in mathematical analysis.
Is this correct?
- #2
- 20,815
- 28,446
Yes.angela107 said:
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