import math


def objective(x):
    """
    Function whose minimum we approximate.
    """
    return (
        math.sin(1.7 * x)
        + 0.4 * math.cos(3.1 * x)
        + 0.15 * (x - 1.5) ** 2
        + math.tanh(x - 0.5)
    )


def numerical_derivative(x, h=0.0001):
    """
    Approximate the derivative of objective at x.
    """
    # TODO: implement this function
    pass


def find_minimum(start, learning_rate, steps, h=0.0001):
    """
    Use numerical derivatives and gradient descent to approximate a local minimum.
    """
    # TODO: implement this function
    pass


if __name__ == "__main__":
    # Simple example for manual testing
    result = find_minimum(0.0, 0.05, 80)
    print(result)
