(c) A differentiable function in an interval (a,b) is concave u... | Filo

Differentiability at a point: algebraic (function isn't differentiable)

SOLVED:(a) Use the Mean-Value Theorem to show that if f is differentiable on an interval, and if |f^'(x)| ≤M for all values of x in the interval, then |f(x)-f(y)| ≤M|x-y| for all values of x and y in the interval. (b) Use the result in part (a) to show that |sinx-siny| ≤|x-y| for all real values of x and y