Julia dot vectorization - how deep into call chain do I need to vectorize?

I'm trying to grok Julia's dot vectorization syntax with a very simple example of a linear interpolating spline.

function createlookup(xk)
    min_i = 1
    max_i = size(xk, 1) - 1
    function inner(x)
        max(min(searchsorted(xk, x).stop, max_i), min_i)
    end
    inner
end


function linear_dydx(x, y)
    diff(y, dims=1) ./ diff(x, dims=1)
end


function linear(xₖ, yₖ)
    segment = createlookup(xₖ)
    dydxₖ = linear_dydx(xₖ, yₖ)
    function inner(x)
        i = segment(x)
        y = yₖ[i] + dydxₖ[i] * (x - xₖ[i])
    end
    inner
end


function main()
    xₖ = [0.0, 1.0, 2.0, 4.0]
    yₖ = [0.0, 2.0, 10.0, 13.0]
    interpolator = linear(xₖ, yₖ)

    x = [i/2.0 for i=0:10]

    println(interpolator(2.43))
    println(interpolator.(x))
end

main()

How deep in the call chain do I need to use the dot notation to make sure my main() call to interpolator.(x) is fully vectorized by the interpreter?

• Does createlookup need any vectorization?
• Is linear_dydx already vectorized via diff and ./?
• Do I need @. in front of y = yₖ[i] + dydxₖ[i] * (x - xₖ[i])?

I find myself throwing dots everywhere and nowhere and am not quite sure how to check whether I'm capturing everything while still preserving the broadcasting flexibility that dot notation is supposed to preserve.