Recent content by Janez25

Ok, I have it now. Thanks!

Homework Statement Suppose f:(-1,1)→R is three times differentiable on the interval. Assume there is a positive value M so that ⎮f(x)⎮ ≤ M⎮x⎮³ for all x in (-1,1). Prove that f(0)=f'(0)=f"(0)=0. Homework Equations The Attempt at a Solution My professor started us off...

Homework Statement Suppose f:R→R and g:R→R are both differentiable and that f'(x)=g(x) and g'(x)=-f(x) for all x ∈ R; f(0)=0 and g(0)=1. Prove : (f(x))²+(g(x))²=1 for all x ∈ R. Homework Equations The Attempt at a Solution I know I need the find d/dx[f(x)²+g(x)²]=d/dx[1], but I...

Homework Statement For all real numbers a and b, define g(x) = 3x² if x≤1, a+bx if x>1. For what values of a and b is g differentiable at x=1? Homework Equations The Attempt at a Solution g(x) is continuous: lim as x→1- [f(x)] = 1; lim as x→1+ [f(x)] = a+b g(x) is...

So, f(a/b)=ma/b. I hope this is right, because this assignment is due at 6:35p.m. I will try to finish on my own. Thanks for everyone's help!

Ok, f(p/q)=f(p+1/q)=f(p)+f(1/q)=f(1/q+1/q)+f(1/q)=?

Ok, does the first part = mn, and the second part = m/n? My professor also mentioned that for part (a) we should also include the proof that f(a/b)=af(1/b). For that part of (a) I have f(a/b)=f(a+1/b)=f(a)+f(1/b)=? This is where I got lost.

Ok, the first part is f(1)=pm, and the second part is f(1/n)=p(m/n). I guess? I am starting to feel about this problem the way my Algebra II students feel about their homework assignments. It is really giving me grief. I know the proof is probably very simple, but the more I think about the...

Is the first part mf(n)? Is the second part mf(1/n)?

My professor suggested using f(3/2) = f(1+1/2) = f(1) + f(1/2) = f(1/2 + 1/2) + f(1/2) = f(1/2) + f(1/2) + f(1/2) = 3f(1/2). I guess I am having so much difficulty with this problem because I do not understand what it is really asking me to prove. I really need this broken down. It takes me a...

Thanks for your help!

Thanks so much for all your help!

How would I write this up as a formal proof?

I am not sure what property I should use. I also am not sure how to show that either function does not attain a maximum value on the interval [0,1) formally.

Thanks! I feel so special now. :blushing: