Applications of differentiation

What you'll learn

1. 1

   Imagine a car 🚗 driving along a road. The speedometer tells you how fast it's going at any moment — that's the derivative, or gradient!

2. 2

   What does the derivative tell you about a curve at a point?

3. 3

   Let's find the gradient of the curve y = x² at x = 3.

4. 4

   Now you try! Find the gradient of y = x² at x = 5 using the slider.

5. 5

   If dy/dx = 3x², what is the gradient at x = 2?

6. 6

   A ball is thrown upward. Its height h(t) = 20t - 5t². Find its velocity at t = 2 seconds.

7. 7

   The derivative of a function gives you the...