Numerical Function Minimization via Gradient Descent

Write a function that takes an arbitrary differentiable function $f(x)$ as its argument and finds a value $x$ that minimizes $f(x)$. You should implement a numerical solution using gradient descent. Specifically: 1. Implement gradient descent using a numerical approximation to the derivative. 2. Discuss the tradeoffs between forward difference and central difference for approximating $f'(x)$. 3. Describe at least two enhancements that improve convergence (e.g., adaptive step size, Newton's method). **Constraints:** - $f$ is a scalar function $\mathbb{R} \to \mathbb{R}$ - Assume $f$ is differentiable and has at least one local minimum - You do not have access to an analytic derivative