Rolle

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Rolles Theorem and the Mean Value Theorem

• Section 3.2

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After this lesson, you should be able to

• Understand when and how to use Rolles Theorem
• Understand when and how to use the Mean Value
  Theorem.

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Rolles Theorem
If f(a) f(b)
Then There is a c in (a, b) such that f (c) 0.
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Example
Determine whether Rolles Theorem can be applied
to each function on the closed interval a, b.
If so, find all values of c in (a, b) such that f
(c) 0.
1)
Is f continuous on -2, 3 and differentiable on
(-2, 3)?
Is f(-2) f(3)?
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Example
1) Continued
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Example
2)
Does Rolles Theorem apply?
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Example
3)
Check out the graph on your calculator.
Does Rolles Theorem apply?
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Mean Value Theorem- MVT
The tangent line at x c is parallel to the
secant line through the endpoints.
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Example
If appropriate, apply the MVT and find the
value(s) of c that fits the theorem.
1)

• Does MVT apply?
• Is f continuous on -1, 1?
• Is f differentiable on (-1, 1)?

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Example
1) Continued
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Example
2)

• Does MVT apply?
• Is f continuous on 1/2, 2?
• Is f differentiable on (1/2, 2)?

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Example
2) Continued
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Homework
Section 3.2 page 176 11-15 odd, 19, 39, 41, 45,
47, 73-76 all