# derivatives's questions - English 1answer

18.020 derivatives questions.

### 2 Real Analysis - Uniform continuity

Prove that if $f: (a,b) \rightarrow \Re$ is differentiable on the open interval $(a,b)$, and $f'(x)$ is bounded on the interval $(a,b)$, then $f$ is uniformly continuous on $(a,b)$. Also, prove the ...

### Sums of equidifferentiable functions are themselves equidifferentiable?

0 answers, 8 views derivatives sequence-of-function

### Are the following conditions enough for showing monotonicity in $[M,\infty]$

2 answers, 47 views calculus real-analysis derivatives
Given: $f$ has a derivative for every $x \in (0,\infty)$ $f'(x) > x$ for every $x>0$ Can I prove that there exists an $M \in \mathbb R$, such that $f(x+1) - f(x)$ is a monotonic increasing ...