Question

Let f(x) be a function defined on (-a, a) with a> 0. Assume that f(x) is continuous at x = 0 and lim_(x →0) (f(x) - f(kx))/x = α, where k ∈ (0, 1) then compute f'(0⁺) and f'(0^-), and comment upon the differentiability of f at x = o.   

Answer 1

∴ f'(0) = f'(0^-) = f'(0⁺) = α/(1 - k)