1. Verify that the function satisfies the three
hypotheses of Rolle's
Theorem on the given
interval. Then find all
numbers c that satisfies the
conclusion of Rolle's
The orem.
y=-x^3+ 4x^2 – 3 ; [0, 4]

0 and 8/3

Step-by-step explanation:

y is continuous on [0,4]

It also also differentiable on (0,4)

Plugging in 0 and 4, we get -3 both times so y(0) = y(4).

Therefore there is at least one value c between 0 and 4 inclusive where y'(c) = 0

y' = -3x^2 + 8x

Set that to 0:

-3x^2 + 8x = 0

x(-3x+8) = 0

x = 0 or 8/3

And both values work.

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.

step-by-step explanation: