Verify that the function satisfies the three hypotheses of rolle's theorem on the given interval. then find all numbers c that satisfy the conclusion of rolle's theorem. (enter your answers as a comma-separated list.) f(x) = x3 − x2 − 6x + 2, [0, 3] c =

Step-by-step explanation:

There are 3 conditions that must be satisfied:

If ALL of those conditions are satisfied, then there exists a value "c" such that c lies between a and b and f'(c) = 0.

f(x) = x³ - x² - 6x + 2     [0, 3]

1. There are no restrictions on x so the function is continuous

2. f'(x) = 3x² - 2x - 6 so the function is differentiable

3. f(0) =  0³ - 0² - 6(0) + 2 = 2

   f(3) =  3³ - 3² - 6(3) + 2  = 2

   f(0) = f(3)

f'(x) = 3x² - 2x - 6 = 0

This is not factorable so you need to use the quadratic formula:

Only one of these values (1.8) is between 0 and 3.

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign