Gradients and tangents to curves

What you'll learn

1. 1

   Imagine you're cycling up a hill. The steeper the hill, the harder you have to pedal! 🚴

2. 2

   What does the gradient of a curve tell you?

3. 3

   Drag the point along the curve. See how the tangent line changes steepness? 📈

4. 4

   Let's find the gradient of this curve at x = 2. 📝

5. 5

   What is the gradient if the tangent goes up 4 units and across 2 units?

6. 6

   Now you try! The tangent at x = 1 goes through (0, 2) and (2, 6). What's the gradient? 🤔

7. 7

   A tangent line that is horizontal (flat) has a gradient of...