Consider the function /(z) = = on the interval [4, 7). Find the average or

mean slope of the function on this interval,

Preview

By the Mean Value Theorem, we know there exists a e in the open interval

(4, 7) such that f'(c) is equal to this mean slope. For this problem, there is

only one c that works. Find it.

Preview

If we apply Rolle's Theorem to the function /(x) = 2 - 8x - 4 on the

interval [0, 4], how many values of c exist such that /'(c) = 0?

Preview

What is the value of c?

Preview

If we try to apply Rolle's Thorem to the function /(z) = 2r- 8x - 4 on

the interval [ - 3, 11], which of the following conditions is not met?

. differentiability on [ - 3, 11]

Of(a) # f(b)

O continuty on [ - 3, 11]

Consider the function /(x) = 2x3 - 913 - 24x + 2 on the interval

[ - 6, 10). Find the average or mean slope of the function on this interval.

Preview

By the Mean Value Theorem, we know there exists a e in the open interval

( - 6, 10) such that f'(c) is equal to this mean slope. For this problem, there

are two values of c that work.

The smaller one is

Preview

and the larger one is

Preview