Rolle's Theorem is not applied to the function f(x)= sin x in [-1,1], because
Understand the Problem
The question is asking for the reason why Rolle's Theorem cannot be applied to the function f(x) = sin x over the interval [-1, 1]. This involves understanding the conditions required for Rolle's Theorem to hold, specifically checking if the function is continuous, differentiable, and if the values at the endpoints of the interval are equal.
Answer
Rolle's Theorem can be applied.
Rolle's Theorem can be applied to the function f(x) = sin(x) on the interval [-1, 1], as it is continuous and differentiable on this interval.
Answer for screen readers
Rolle's Theorem can be applied to the function f(x) = sin(x) on the interval [-1, 1], as it is continuous and differentiable on this interval.
More Information
For f(x) = sin(x) in the interval [-1, 1], the function is both continuous and differentiable everywhere. The sine function is smooth and has no points of non-differentiability.
Tips
A common mistake is confusing the absolute value function with sine. Ensure the function in question is clearly identified.
Sources
- Rolle's theorem is not applicable for the function f(x)=|x| in the interval - toppr.com
- Rolle's theorem violation or not? - Mathematics Stack Exchange - math.stackexchange.com
- 3.6: The Mean Value Theorem - Mathematics LibreTexts - math.libretexts.org
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