Or the function f(x)=x− 5 x , find all values of c in the interval [2,4] that satisfy the conclusion of the Mean-Value Theorem. If appropriate, leave your answer in radical form. Enter all fractions in lowest terms

Therefore the value of c is

Step-by-step explanation:

Mean Value Theorem:

It state that if f(x) is defined

(i) f(x) continuous on the interval [a,b]

(ii) f(x) differentiable on (a,b).

then there exist a one number c∈ (a,b) such that

Here

(i) f(x) is continuous on [2,4]

Since it is discontinuous at 0 and 0∉[2,4].

(ii)   which is exist x≠0 and 0∉(2,4).

Therefore f(x) is differentiable on (2,4)

f(x) satisfies the Mean Value Theorem,

Then there exist a number c∈(2,4) such that

Therefore the value of c is

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3

to find the unit price, we must figure out the cost of one item (in this case one dish towel).   to do this, we divide the total price ($7.92) by the number of items bought (for this problem it is 8, because there are eight dish towels in one pack).  

$7.92/8 = $0.99

therefore, the unit price, or the price of one dish towel, is $0.99.

hope this !