Let k(x) = h(x) - g(x), where g and h are infinitely differentiable functions from R to R. Define f(n) to be the nth derivative of a function mapping R to R. Suppose hn(x) = gn(x) for all x. Suppose k(x1) =  k(x2) = ... = k(xn) = 0 for x1 < x2 < x3 < ...  < xn . Show that g = h.

Let k(x) = h(x) - g(x), where g and h are infinitely differentiable functions from R to R. Define f⁽ⁿ⁾ to be the n^th derivative of a function mapping R to R. Suppose hⁿ(x) = gⁿ(x) for all x. Suppose k(x₁) =  k(x₂) = ... = k(x_n) = 0 for

x₁ < x₂ < x₃ < ...  < x_n . Show that g = h.