Prove: If f(x) is a continuous function on a closed interval [a, b] and x1, x2, ..., xn are n points in the interval, then there exists c such that:
Any ideas?
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Prove: If f(x) is a continuous function on a closed interval [a, b] and x1, x2, ..., xn are n points in the interval, then there exists c such that:
Any ideas?
Hint: intermediate value theorem, showing that the average ofis between
and
.
Note how to use subscripts, [TEX]f(c)=\frac{f(x_1)+f(x_2)+...+f(x_n)}{n}[/TEX] givesQuote:
Originally Posted by loui1410
Prove: If f(x) is a continuous function on a closed interval [a, b] and x1, x2, ..., xn are n points in the interval, then there exists c such that:
.
Let. Do you see that
.
Can you use the intermediate value theorem?