ML Katas

Imagine a simple 1D function $f(x)=x^2-4x+5$. Your goal is to find the minimum of this function using Gradient Descent.

1. Derive the gradient: What is $\frac{df}{dx}$?
2. Perform a few steps: Starting at $x_0=0$, and using a learning rate $\alpha =0.1$, calculate the next three steps ($x_1,x_2,x_3$).
3. Intuition: Describe in your own words what is happening at each step. How does the magnitude of the gradient influence the step size?
4. Verification: You can plot the function and mark the points you calculated. Also, find the analytical minimum of the function and compare it to your result after a few steps. Does it converge towards the minimum?