Question

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

Answer 1

`y = (1-x)/(2ln2)`
or
`y = log_2e/2(1-x)`

Explanation:

`f(x)=-x(1-x)ln4=2x(x-1)ln2`
`f^'(x)=2ln2(2x-1)`
`f^'(1)=2ln2`
`f(1)=0`
`m_(|--)=-1/(f^'(1))=-1/(2ln2)=-log_2e/2`
`y = -1/(2ln2)(x-1)`