Suppose n > 1 is a positive integer. Prove for all x > 1.
(hint: suppose we know f and g are differentiable on the interval (-c,c) and f(0) = g(0), if f'(x) > g'(x) for all , then f(x) > g(x) for all .
What you want to do is use the hint on a base case (n=2). Then you will make the assumption that the problem hypothesis holds for n=k. Use this assumption to prove that it is true for n=k+1.
What you want to do is use the hint on a base case (n=2). Then you will make the assumption that the problem hypothesis holds for n=k. Use this assumption to prove that it is true for n=k+1.
Suppose n > 1 is a positive integer. Prove for all x > 1.
(hint: suppose we know f and g are differentiable on the interval (-c,c) and f(0) = g(0), if f'(x) > g'(x) for all , then f(x) > g(x) for all .
Note that if and . That and and the concluso follows.