Where does a polynomial rise?

You will write three functions for a polynomial given by its coefficients, highest power first: $[1, -6, 9, 2]$ means $x^3 - 6x^2 + 9x + 2$. The checker tests several polynomials.

The idea. The derivative of $a_nx^n$ is $na_nx^{n-1}$. The function is increasing where the derivative is positive. The derivative can change sign only at its zeros, so we find those and test between them.

Your tasks.

1. Finish derivative(coeffs). Return the coefficients of the derivative, in the same order.
2. Finish stopping_points(coeffs). Return the sorted real zeros of the derivative, rounded to 6 decimals.
3. Finish rising(coeffs, x). Return True if the function is increasing at x, and False otherwise.