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Understanding the Mean Value Theorem in Calculus

Learn about the Mean Value Theorem, continuous functions, finding slopes, derivatives, and drawing tangent lines in calculus.

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Understanding the Mean Value Theorem in Calculus

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  1. Mean Value Theorem

  2. Mean Value Theorem Suppose f(x)=

  3. Mean Value Theorem Suppose f(x)= x y 0 0

  4. Mean Value Theorem Suppose f(x)= x y 0 0 1 1

  5. Mean Value Theorem Suppose f(x)= x y 0 0 1 1 2 8

  6. Mean Value Theorem Suppose f(x)= x y 0 0 1 1 2 8 -1 -1

  7. Mean Value Theorem Suppose f(x)= x y 0 0 1 1 2 8 -1 -1 -2 -8

  8. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y 0 0 1 1 2 8 -1 -1 -2 -8

  9. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y Draw line from -2 to 2 0 0 1 1 2 8 -1 -1 -2 -8

  10. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y Draw line from -2 to 2 0 0 1 1 2 8 -1 -1 -2 -8

  11. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y Draw line from -2 to 2 0 0 Find slope of line: 1 1 2 8 -1 -1 -2 -8

  12. Mean Value Theorem Suppose f(x)= (2,8) F(x) is continuous on [-2,2] x y Draw line from -2 to 2 0 0 Find slope of line: 1 1 2 8 -1 -1 -2 -8 (-2,-8)

  13. Mean Value Theorem Suppose f(x)= (2,8) F(x) is continuous on [-2,2] x y Draw line from -2 to 2 0 0 Find slope of line: 1 1 2 8 -1 -1 -2 -8 (-2,-8)

  14. Mean Value Theorem Suppose f(x)= (2,8) F(x) is continuous on [-2,2] x y Draw line from -2 to 2 0 0 Find slope of line: 1 1 2 8 -1 -1 -2 -8 (-2,-8)

  15. Mean Value Theorem Suppose f(x)= (2,8) F(x) is continuous on [-2,2] x y Draw line from -2 to 2 0 0 Find slope of line: 1 1 2 8 -1 -1 Find derivative and set = 4 -2 -8 (-2,-8)

  16. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y Draw line from -2 to 2 Find slope of line: 0 0 1 1 2 8 -1 -1 -2 -8 Find derivative and set = 4

  17. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y Draw line from -2 to 2 Find slope of line: 0 0 1 1 2 8 -1 -1 -2 -8 Find derivative and set = 4

  18. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y Draw line from -2 to 2 Find slope of line: 0 0 1 1 2 8 -1 -1 -2 -8 Find derivative and set = 4

  19. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y Draw line from -2 to 2 Find slope of line: 0 0 1 1 2 8 -1 -1 -2 -8 Find derivative and set = 4

  20. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y Draw line from -2 to 2 Find slope of line: 0 0 1 1 2 8 -1 -1 -2 -8 Find derivative and set = 4

  21. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y Draw line from -2 to 2 Find slope of line: 0 0 1 1 2 8 -1 -1 -2 -8 Find derivative and set = 4 Draw tangent lines

  22. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y Draw line from -2 to 2 Find slope of line: 0 0 1 1 2 8 -1 -1 -2 -8 Find derivative and set = 4 Draw tangent lines

  23. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y Draw line from -2 to 2 Find slope of line: 0 0 1 1 2 8 -1 -1 -2 -8 Find derivative and set = 4 Draw tangent lines

  24. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y Draw line from -2 to 2 Find slope of line: 0 0 1 1 2 8 -1 -1 -2 -8 Find derivative and set = 4

  25. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y Draw line from -2 to 2 Find slope of line: 0 0 1 1 2 8 -1 -1 -2 -8 Find derivative and set = 4

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