# How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [11, 23] for #f(x) = sqrt (x-7)#?

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To determine all values of ( c ) that satisfy the conclusion of the Mean Value Theorem (MVT) on the interval ([11, 23]) for ( f(x) = \sqrt{x - 7} ), follow these steps:

- Compute the derivative of ( f(x) ), denoted as ( f'(x) ).
- Find the average rate of change of ( f(x) ) on the interval ([11, 23]) using the formula ( \frac{f(23) - f(11)}{23 - 11} ).
- Find the value of ( c ) that makes the derivative equal to the average rate of change computed in step 2. This is done by setting ( f'(c) = \frac{f(23) - f(11)}{23 - 11} ).
- Solve for ( c ) to find all values that satisfy the conclusion of the Mean Value Theorem.

By following these steps, you can determine all values of ( c ) that satisfy the conclusion of the Mean Value Theorem on the interval ([11, 23]) for ( f(x) = \sqrt{x - 7} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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