(3) A function f: (a, b) ? R is convex if f(x + (1 - A)y) ? (x) + (1 ? x)f(y) (Vx, y ? (a, b), VA (0,1)) Provide an example of a convex function on R that is not of the form f(x) = rx+s for real numbers r and s. Also, prove that any nondecreasing convex function on any open interval (a, b) is continuous.

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(3) A function f: (a, b) ? R is convex if f(x + (1 - A)y) ?  (x) + (1 ? x)f(y) (Vx, y ? (a, b), VA  (0,1)) Provide an example of a convex function on R that is not of the form f(x) = rx+s for real numbers r and s. Also, prove that any nondecreasing convex function on any open interval (a, b) is continuous.

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(Solved): (3) A function f: (a, b) R is convex if f(x + (1 - A)y) \(x) + (1 x)f(y) (Vx, y ...

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