# The Mean Value Theorem Exercises

### Example 1

For the given function and interval, determine if we're allowed to use the Mean Value Theorem for the function on that interval. If so, what does the Mean Value Theorem let us conclude?

• f(x) = x3 on (-1,1)

### Example 2

For the given function and interval, determine if we're allowed to use the Mean Value Theorem for the function on that interval. If so, what does the Mean Value Theorem let us conclude?

• f(x) = \frac{1}{x2} on (1,2)

### Example 3

For the given function and interval, determine if we're allowed to use the Mean Value Theorem for the function on that interval. If so, what does the Mean Value Theorem let us conclude?

•  f(x) = \sqrt{x} on (0,4)

### Example 4

For the given function and interval, determine if we're allowed to use the Mean Value Theorem for the function on that interval. If so, what does the Mean Value Theorem let us conclude?

• f(x) = 0 on (2,3)