Sender: JT Wilkins
Subject: a Calculus question
Pleeeeeeeeeease help me!!!
These are the questions:
Thank you very much,
- Show that there exists a unique function that meets the following requirements:
a) f is differentiable everywhere
b) f(0)= f'(0)= 0
c) f(x+y)= f(x)+ f(y), for all real values of x,y
- Consider the function
F: R-->R (All Reals)
F(x) = 0, for x irrational & 1/q, x=p/q gcd(p,q)=1 q > 0
a)determine the values x where f is continuous, respectively discontinuous.
b)determine the values x when f is differentiable and for each of these values compute f'(x).
Here is a hint for problem 1. Write the definition for the derivative of f at x. Use requirement c) to show that f'(x) does not depend on x. Since f'(x) does not depend on x, f'(x) is a constant. But f"(0) = 0 and thus f'(x) = 0 for all x.