Verify that the fucntion satisfies the three hypotheses of rolles theorem on the given interval . then find all numbers c that satisfy the conclusion . f(x)= x^3-2x^2-4x+2 . [ -2,2]

The roots of the polynomial x^3 − 2x^2 − 4x + 2 are:

x1 = 0.42801

x2 = −1.51414

x3 = 3.08613

x1 and x2 are in the desired interval [-2, 2]

f'(x) = 3x^2 - 4x - 4

so we have:

3x^2 - 4x - 4 = 0

x = ( 4 +- √(16 + 48) )/6

x_1 = -4/6 = -0.66

x_ 2 = 2

According to Rolle's theorem, we have one point in between:

x1 = 0.42801 and x2 = −1.51414

so we see that Rolle's theorem holds in our function.

10 miles

step-by-step explanation:

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: