Proving Differentiability of f given g'(x) < 0 $\forall$ x

  • Thread starter Thread starter mathwizarddud
  • Start date Start date
  • Tags Tags
    Differentiability
mathwizarddud
Messages
25
Reaction score
0
Suppose the real valued g is defined on \mathbb{R} and g&#039;(x) &lt; 0 for every real x. Prove there's no differentiable f: R \rightarrow R such that f \circ f = g.
 
Physics news on Phys.org

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Prove ##a + b = b + a## using Peano postulates
Replies
3
Views
1K
Show function series involving arctan is not differentiable at x=0
Replies
26
Views
2K
Prove ##(a+b) + c = a + (b+c)## using Peano postulates
Replies
9
Views
2K
Prove ##1 + a=s(a)=a+1## for ##a \in \mathbb{N}##
Replies
1
Views
1K
Prove ##(a\cdot b)\cdot c =a\cdot (b \cdot c)## using Peano postulates
Replies
1
Views
1K
Prove ##(a+b)\cdot c=a\cdot c+b\cdot c## using Peano postulates
Replies
3
Views
1K
Prove limit comparison test for Integrals
Replies
2
Views
2K
Problem 1-23 and 1-24 from Spivak's Calculus on Manifolds
Replies
6
Views
2K
Prove if ##a\cdot c = b \cdot c## then ##a = b## using Peano postulates
Replies
2
Views
1K
Prove that ##\lim\limits_{x \to \infty} f(x) = 0##
Replies
3
Views
515

Hot Threads

Recent Insights

Back
Top