Is f(x)=sqrt(x+2) increasing or decreasing at x=2 ?

1 Answer
Mar 19, 2016

f(x)=sqrt(x+2 is increasing at x=2

Explanation:

To find whether f(x)=sqrt(x+2 is increasing or decreasing at x=2, first differentiate f(x)

As f(x)=sqrt(x+2 can be written as f(x)=(x+2)^(1/2), hence

(df)/(dx)=1/2(x+2)^(1/2-1)=1/2(x+2)^(-1/2)=1/(2sqrt(x+2)

At x=2,

(df)/(dx)=1/(2sqrt(2+2))=1/4

As it is positive, f(x)=sqrt(x+2 is increasing at x=2