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