Mean value of a function

What you'll learn

1. 1

   Imagine you're tracking the speed of a car 🚗 over a 60-second journey. The speed changes every second — sometimes fast, sometimes slow. The 'mean value' of the speed function tells you the AVERAGE speed over the whole trip.

2. 2

   What does the mean value of a function represent?

3. 3

   Drag the slider to see how the function's height changes. The mean value is like the 'middle height' of the curve above the x-axis.

4. 4

   Find the mean value of f(x)=x² from x=0 to x=2.

5. 5

   For a function f(x), the mean value from a to b is:

6. 6

   Try it: estimate the mean value of f(x)=x from x=0 to x=4. The area under the curve is a triangle: base=4, height=4, area=8.

7. 7

   What is the mean value of f(x)=x from 0 to 4? (Area=8, width=4)