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 ) = cos 3 x , [ π / 12 , 7 π / 12 ]

The number c= satisfies conclusion of Roller's theorem.

Step-by-step explanation:

Given function is,

which is,

(1) continuous on the closed interval . Since,

and,

(2) derivable in the open interval because of continuity.

(3)

Hence all conditions of Rollr's theorem satisfied, so there exist at least one value c, where such that,

where n is an integer.

When,

n=1, c=

n=2, c=

Similarly for other values of n, c lies outside of the given interval.

Hence c= satisfies conclusion of Roller's theorem.

a box 3 3/4 feet long or 4+ feet.

step-by-step explanation:

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)