Help with symbolics, how to get coefficients and simple roots

using Symbolics

@variables x
D = Differential(x)
Z = 2.1309 + 0.0515x - 0.0009(x^2)
ZZ = expand_derivatives(D(Z))

# Derivative is 0.0515 - 0.0018x
println("Derivative is ",ZZ)

# How to get the coefficient of x from equation ZZ

# Question 1, how do I get the coefficient of x^0 which is 0.0515
#coefficient_x0 = ???

# Question 2, how do I get the coefficient of x^1 which is -0.0018
#coefficient_x1 = ???

# question 3, How do I find the root of the derivative which is 28.611
# derivative_root = ???

How to extract the coefficients of x from ZZ dynamically?

I think someone recently asked for a coeff function but it doesn’t exist yet.

Linear rootfinding is done via solve_for.

In math the solution to get the coefficients of a variable is to take the derivative with respect to the variable and set any residues of the variable to zero. Hopefully there is a better method without resorting to taking derivatives but until then that was my solution:

function mycoeffs(f,var,order)
    if order == 0
        return substitute(f,Dict(var=>0))
    return substitute(newf,Dict(var=>0))

You can test it with something like: