# What is the equation of the normal line of f(x)= -xln(4^(1-x)) at x = 1?

Oct 28, 2016

$y = \frac{1 - x}{2 \ln 2}$
or
$y = {\log}_{2} \frac{e}{2} \left(1 - x\right)$

#### Explanation:

$f \left(x\right) = - x \left(1 - x\right) \ln 4 = 2 x \left(x - 1\right) \ln 2$
${f}^{'} \left(x\right) = 2 \ln 2 \left(2 x - 1\right)$
${f}^{'} \left(1\right) = 2 \ln 2$
$f \left(1\right) = 0$
${m}_{\vdash} = - \frac{1}{{f}^{'} \left(1\right)} = - \frac{1}{2 \ln 2} = - {\log}_{2} \frac{e}{2}$
$y = - \frac{1}{2 \ln 2} \left(x - 1\right)$