Question

Show that a number δ exists between x1 and x2 with
f(δ) = ( f(x1) + f(x2) ) / 2

Answer 1

The Intermediate Value Theorem can be used to show that a number δ exists between x1 and x2 with f(δ) = ( f(x1) + f(x2) ) / 2.

Step-by-step explanation:

To show that a number δ exists between x1 and x2 with f(δ) = ( f(x1) + f(x2) ) / 2, we can use the Intermediate Value Theorem.

The Intermediate Value Theorem states that if a function is continuous on the interval [a, b] and takes on two different values, f(a) and f(b), then it must also take on every value between f(a) and f(b).

In this case, since f(x) = ( f(x1) + f(x2) ) / 2, we have f(x1) < f(δ) < f(x2). Therefore, there must exist a number δ between x1 and x2 such that f(δ) = ( f(x1) + f(x2) ) / 2.