Numerical methods

What you'll learn

1. 1

   Numerical methods help us find approximate answers to tricky equations that can't be solved exactly — like finding where a wobbly graph crosses the x-axis. 📈

2. 2

   Why do we use numerical methods?

3. 3

   Let's use the 'change of sign' method to find a root of x³ - 2x - 5 = 0. We'll test x = 2 and x = 3. 📝

4. 4

   Try x = 2.5 for the same equation. Is it positive or negative? Drag the point on the number line to 2.5. 🎯

5. 5

   At x = 2.5, what is the value of x³ - 2x - 5?

6. 6

   Since f(2.5) = -1.875 (negative) and f(3) = 16 (positive), the root is between 2.5 and 3. Let's narrow it down! 🎯

7. 7

   Now test x = 2.625. Drag the point to 2.625 on the number line to check if it's positive or negative. 🧭

8. 8

   After testing x = 2.625, the sign is still negative. Where is the root now?