- #1

rainwyz0706

- 36

- 0

Let g : T → R be the function deﬁned by g(x, y) =(f (x)−f (y))/(x-y)

1.Prove that g(T ) ⊂ f (I) ⊂ g(T ) (The last one should be the closure of g(T), but I can't type it here)

2. Show that f ′ (I) is an interval.

I don't know what the closure of g(T) is, so I can't prove the second part in question 1. To show that f ′ (I) is an interval, I intend to show that it's connected, f(x) is continuous. Would that work? Or do I need to use g(t) is continuous to show that?

Your help is greatly appreciated!