Let b > 0 and f : [0, b] â R be continuous and f(b) = 0. Assume that f is differentiable on (0, b). Show: For every n â N, there exists some c â (0, b) such that cf â²(c) = ânf(c).
Hint: Apply Rolleâs theorem to the function g(x) = xn f(x).
5.2.10. Let b > 0 and f : [0, b] â R be continuous and f(b) = 0. Assume that f is differentiable on (0, b). Show: For every n N, there exists some c (0, b) such that cf,(c) -nf(c). Hint: Apply Rolle's theorem to the function g(x)f(x)
