Question

What is the equation of the normal line of `f(x)=xln(3^(1/x))` at `x=0`?

Answer 1

`x=0`

Explanation:

`f(x)=xln(3^(1/x))=ln(3^(x*1/x))=ln(3^1)=ln(3)` (power rule for logarithms)

since `ln(3)` is a constant, `f(x)` is a horizontal line. therefore the line normal to `f(x)` must be vertical, so it follows the format: `x=a`

since the line is normal to `f(x)` at x=0, 0=a.

so the normal line is simply: `x=0`