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Questions and Answers
What is the definition of Rolle's theorem?
What is the definition of Rolle's theorem?
Rolle's theorem states that if a function crosses the x-axis and the cost of the x-axis again, and it's continuous between those points, then at least one point between those two points, the slope will be equal to zero.
What must be certain about the slope between the two points in Rolle's theorem?
What must be certain about the slope between the two points in Rolle's theorem?
At least one point between the two points, the slope will be equal to zero.
What conditions must be met for Rolle's theorem to apply?
What conditions must be met for Rolle's theorem to apply?
The function must cross the x-axis and the cost of the x-axis again, and it must be continuous between those points.
![Rolle's Theorem for f(x) = x^2 in [-1, 1]](https://images.unsplash.com/photo-1570914755800-cc174d78aa6b?crop=entropy&cs=srgb&fm=jpg&ixid=M3w0MjA4MDF8MHwxfHNlYXJjaHwxfHxSb2xsZSUyN3MlMjBUaGVvcmVtJTJDJTIwY2FsY3VsdXMlMkMlMjBtYXRoZW1hdGljc3xlbnwxfDB8fHwxNzI3MTAzNzY3fDA&ixlib=rb-4.0.3&q=85&w=300&fit=crop&h=200&q=75&fm=webp)
