def centered_difference_quotient(f, pts, h=1e-5):
    """Compute the centered difference quotient for function (f)
    given points (pts).

    Inputs:
        f (function): the function for which the derivative will be approximated
        pts (array): array of values to calculate the derivative

    Returns:
        centered difference quotient (array): array of the centered difference
            quotient
    """
    Df_app = lambda x: .5*(f(x+h)-f(x-h))/h
    return Df_app(pts)