Question

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

Answer 1

`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`