Calculus Theorems and Rules

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First derivative rule

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A rule in calculus that provides information about the slope of the tangent line to a curve at a given point.

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Second derivative rule

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A rule in calculus that provides information about the concavity of a function and the nature of its critical points.

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Rolle's Theorem

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A theorem in calculus that states if a differentiable function has equal values at two points, there exists at least one point between them where the first derivative is zero.

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MVT (Mean Value Theorem)

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A theorem in calculus that states if a function is continuous on a closed interval and differentiable on the open interval, there exists at least one point where the derivative equals the average rate of change over the interval.

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IVT (Intermediate Value Theorem)

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A theorem in calculus that states if a function is continuous on a closed interval, it takes on every value between its values at the endpoints of the interval.

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EVT (Extreme Value Theorem)

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A theorem in calculus that states if a function is continuous on a closed interval, it must attain a maximum and a minimum value on that interval.