George Saliaris
Junior Member
- Joined
- Dec 15, 2019
- Messages
- 53
Let f: [a,b] - >R a continuous function and the points A(x, f(x)), B(y, f(y), Γ(c, f(c)) Prove that they do exist x1 and x2 such that: ... (see in the picture
My tries :
1) Multiply each side of the inequatily with 0.5 and try to prove an inequatily with areas (no result)
2)Suppose without any loss of generality some relation between x,y, c and/or f(x), f(y), f(c) and then I honestly do not know what to do
3) Apply Bolzano's theorem two 2 times (I highly doubt this is a correct way)
4) Intermediate Value theorem and/or Maximum and Minimum Value Theorem for f(x) considering that f(x1) =M (maximum value of f(x)) and f(x2) = m (where m the minimum value of f(x)) and somehow continue
What I am almost sure about is calculating the
My tries :
1) Multiply each side of the inequatily with 0.5 and try to prove an inequatily with areas (no result)
2)Suppose without any loss of generality some relation between x,y, c and/or f(x), f(y), f(c) and then I honestly do not know what to do
3) Apply Bolzano's theorem two 2 times (I highly doubt this is a correct way)
4) Intermediate Value theorem and/or Maximum and Minimum Value Theorem for f(x) considering that f(x1) =M (maximum value of f(x)) and f(x2) = m (where m the minimum value of f(x)) and somehow continue
What I am almost sure about is calculating the
