R Rob L New member Nov 14, 2010 #1 Assume f is differentiable on (a,b), a<x<a_n<b_n<b, a_n converges to x, b_n converges to x, and (b_n-x)/(b_n-a_n) is bounded. Prove this implies (f(b_n) - f(a_n))/(b_n - a_n) converges to f '(x).
Assume f is differentiable on (a,b), a<x<a_n<b_n<b, a_n converges to x, b_n converges to x, and (b_n-x)/(b_n-a_n) is bounded. Prove this implies (f(b_n) - f(a_n))/(b_n - a_n) converges to f '(x).
