Captain Redbeard's Hidden Treasure
Vectors & Geometry DS practice problem on Onlearn.
Difficulty: medium.
Topics: Understanding Find Captain Redbeard's Hidden Treasure, Power Rule Differentiation, Iterative Parameter Updates, Convergence Thresholding, Learning Rate Selection, Local Minimum Identification, Random Initialization, Calculus, Optimization, Machine Learning, Numerical Analysis, Mathematical Foundations, Gradient-Based Optimization, Differential Calculus, Convergence Analysis, Hyperparameter Tuning, Algorithmic Implementation.
Captain Redbeard, the most daring pirate of the seven seas, has uncovered a mysterious ancient map. Instead of islands, it shows a strange wavy curve, and the treasure lies at the lowest point of the land! (watch out for those tricky local mins) The land's height at any point $x$ is given by: f(x) = x^4 3x^3 + 2 Your Mission: Implement a Python function that finds the value of $x$ where $f(x)$ reaches its minimum, starting from any random initial position.