Question

What is the equation of the line that is normal to `f(x)= (2-x)sqrt( 2x+2)` at `x=2`?

Answer 1

`y=sqrt(6)/6x`

Explanation:

We get by the product and chain rule

`f'(x)=sqrt(2)(-sqrt(x+1)+(2-x)*(1/2)*(x+1)^(-1/2))`

we get `f'(x)=sqrt(2)*(-sqrt(3))=-sqrt(6)`
so we get the slope of the normal line

`m_n=1/sqrt(6)=sqrt(6)/6`

Now we have `f(2)=0`
so our equation is given by

`y=sqrt(6)/6x`