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5.5

MeanValue Theorem. 5.5. If f ( x ) is continuous over [ a , b ] and differentiable over ( a , b ), then at some point c between a and b :. The Mean Value Theorem says that at some point in the closed interval, the actual slope equals the average slope.

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5.5

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  1. MeanValue Theorem 5.5

  2. If f (x) is continuous over [a,b] and differentiable over (a,b), then at some point c between a and b: The Mean Value Theorem says that at some point in the closed interval, the actual slope equals the average slope. Mean Value Theorem for Derivatives The Mean Value Theorem only applies over a closed interval.

  3. Slope of tangent: Slope of secant:

  4. The Mean Value Theorem is actually common sense. Think of it like this. If, on a 2-hour car trip, you averaged 50 miles per hour, then according to the Mean Value Theorem, at least once during the trip, your speedometer actually read 50 mph.

  5. At what x-value(s) on the interval [-2,3] does the graph of satisfy the Mean-Value Theorem?

  6. At what x-value(s) on the interval [-2,3] does the graph of satisfy the Mean-Value Theorem?

  7. At approximately what x-value(s) on the interval [0,7] does the graph of satisfy the Mean-Value Theorem?

  8. Homework Page 285 #1-12 Page 293 #1-5

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