Help with mean value theroem

Question

f(x) = x/(x+4) at [0, 5] Find the number c that satisfies the conclusion of the Mean Value Theorem.? 

Answer 1

Mean value theorem :

If f is

(1) Continuous on closed interval [a,b] where a < b

(2) Differntiable on the open interval (a,b)

then there exist at least one point c in the(a,b) such that .

Step1 :

Given function .

(1) f(x) is continuous on closed interval [0,5] where 0 < 5

(2) f(x) is differntiable on the open interval (0,5)

Step2 :

Condition 1 and 2 are satisfied

So there exist a point c in the (0,5) such that .

where a = 0, b = 5.

Substitute a = 0, b = 5.

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Step3 :

Apply derivative

Apply formula

 

Substitute x = c

Substitute

c^2 +8c - 20 =0

Solution :

The solution is c = 2