# How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=x/(x+2)# on the interval #[1,4]# ?

##### 1 Answer

Sep 12, 2014

The mean value theorem guarantees that there exists a number

The actual value of

Let us find the left-hand side of the above equation,

By Quotient Rule,

Let us find the right-hand side,

By setting the left-hand side and the right-hand side equal to each other,

by taking the reciprocal,

by multiplying by 2,

by taking the square-root,

by subtracting 2,

Since