Course Elementary Analysis Real Analysis Topic Applications

Course: Elementary Analysis (Real Analysis).

Topic : Applications of the Mean Value Theorem.

Suppose f\' is continues on [a, b] and epsilon > 0. Prove that there exists theta > 0 such that |f(t) - f(x)/t - x - f\'(x)|

Solution

Solution:

This is the application of mean value theorem in the closed interval [a,b]

Since f\' is continuous,by definition of continuity,there exists a positive delta such that