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Course: AP??/College Calculus BC?>?Unit 5
Lesson 1: Using the mean value theorem- Mean value theorem
- Mean value theorem example: polynomial
- Mean value theorem example: square root function
- Using the mean value theorem
- Justification with the mean value theorem: table
- Justification with the mean value theorem: equation
- Establishing differentiability for MVT
- Justification with the mean value theorem
- Mean value theorem application
- Mean value theorem review
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Justification with the mean value theorem
Problem
Let .
Below is Rafael's attempt to write a formal justification for the fact that the equation has a solution where .
Is Rafael's justification complete? If not, why?
Rafael's justification:Exponential and trigonometric functions are differentiable and continuous at all points in their domain, andis within 's domain. So, according to the mean value theorem,must have a solution somewhere in the interval .