Thread: Continuity

Prove: If f(x) is a continuous function on a closed interval [a, b] and x₁, x₂, ..., x_n are n points in the interval, then there exists c such that:


Any ideas?

Hint: intermediate value theorem, showing that the average of is between and .

Originally Posted by loui1410

Prove: If f(x) is a continuous function on a closed interval [a, b] and x₁, x₂, ..., x_n are n points in the interval, then there exists c such that:

Note how to use subscripts, [TEX]f(c)=\frac{f(x_1)+f(x_2)+...+f(x_n)}{n}[/TEX] gives .

Let . Do you see that .

Can you use the intermediate value theorem?