✏️ Practice Exercises

Optimization

3 problems · Easy to Hard · Type your working · AI checks your steps

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How to use these exercises

Read the question → work it out step-by-step in the box → click Check My Working to get AI feedback. Use hints if stuck. Reveal the full solution only after you have tried.

01

easy

Minimum of f(x) = x² + 4:

💡 Show hint

x² ≥ 0; minimum when x = 0.

Your Working

02

medium

Find x that minimises f(x) = (x − 5)²

💡 Show hint

Vertex of parabola.

Your Working

03

hard

Gradient descent on f(x) = x² with learning rate 0.1, start x = 5. Value after 1 step?

💡 Show hint

x ← x − α·∇f. ∇f = 2x.

Your Working

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