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

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Answer 1 · 2018-06-25T12:03:03

$y=sqrt(6)/6x$

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

$y=sqrt(6)/6x$

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