(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose f and g are differentiable on R, and f(a) = g(a) and f'(x) <= g'(x) for all x >= a. Show that f(x) <= g(x) for all x >= a. Give a physical interpretation of this result.

Also, using the Mean Value Theorem:

(a) Let f: R --> R be a differentiable function. Suppose that its derivative f'(x) is bounded Prove that f is uniformly continuous.

(b) Let f: R --> R be a differentiable function. Suppose that lim (x --> infinity) f'(x) = infinity. Show that f cannot be uniformly continuous.

(c) Let g(x) = (x)^1/2 show that g'(x) is unbounded on (0,1] but g(x) is uniformly continuous on [0,1].

2. Relevant equations

3. The attempt at a solution

I don't know how to quite formulate the inequalities, any help?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Analysis Homework Help

**Physics Forums | Science Articles, Homework Help, Discussion**