Welcome to Julia Discourse, and thanks for providing your code and stacktrace!
This means you tried to call adjoint on the function f (whose type is typeof(f)), but that method isn’t defined. Even though you didn’t explicitly write adjoint(f) anywhere, you do have
Specifically, f' is parsed as adjoint(f), so an equivalent statement to the above is
x_seq[i] = x_seq[i-1] + eta * adjoint(f)(x_seq[i-1])
It looks like you meant to take the derivative of f, so you should instead write
x_seq[i] = x_seq[i-1] + eta * Dxf(x_seq[i-1])