What is the equation of the normal line of $f (x) = ln 2 x - x$ $f(x)=ln2x-x$ at $x = 4$ $x=4$ ?

Question

2119 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-06T13:45:07

$y = \frac{4}{3} x + 3 ln 2 - \frac{28}{3}$ $y=4/3x+3ln2-28/3$

The equation of the line normal to the curve $y = f (x)$ $y=f(x)$ in the point $x = ¯ x$ $x=bar x$ is given by:

$y=f(bar x) -1/(f'(bar x))(x-barx)$

Given $bar x = 4$ :

$f(x) = ln2x-x$
$f(4) =ln8-4=3ln2-4$

$f'(x) = 1/x-1$
$f'(4) = -3/4$

The equation of the normal line is:

$y=4/3(x-4)+3ln2-4=4/3x+3ln2-28/3$

enter image source here

What is the equation of the normal line of f(x)=ln2x-xf(x)=ln2x−xf(x)=ln2x-x at x=4 x=4x=4 ?