Understanding Rolle's Theorem and The Mean Value Theorem in Calculus

Rolle's Theorem states that for a continuous and differentiable function on a closed interval with equal function values at the endpoints, there exists at least one point where the derivative is zero. The Mean Value Theorem asserts that for a continuous and differentiable function on an interval, there exists a point where the average rate of change equals the instantaneous rate of change.

• Calculus
• Rolles Theorem
• Mean Value Theorem
• Continuity
• Differentiability

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1. 3.2 Rolle s Theorem & The Mean Value Theorem p. 220

2. Rolles Theorem If f is continuous on [a,b] and differentiable on (a, b) and f(a)=f(b), then there is at least one number, c, such that *could be more than one place

3. Mean Value Theorem If f is continuous on [a,b] and differentiable on (a,b) then there exists a number, c, such that: *says the average rate of change must = instantaneous rate of change at some time on [a,b].

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5. Homework p. 224 9-21 EO odd, 25, 37-49 odd, 53, 55, 81-83 all