Continuous on $[a,b]$ and $f'(x)>0$ on $(a,b)$ except for a $c$ in $(a,b)$ then $f$ is strictly increasing
90892
Is a function increasing if the derivative is positive except at one point of an interval?
53627
Proving continuity of $f$
57023
If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$
16212
If $f$ is continuous, nonnegative on $[a, b]$, show that $\int_{a}^{b} f(x) d(x) = 0$ iff $f(x) = 0$
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
151410
Inequality of continuous functions
37966
If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$
151573
Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
52922
let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
150554
proof that $f'$ is continuous at $a$
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
33523
If $f(0)=0$ and $f'$ is increasing, then $\frac{f(x)}{x}$ is increasing.
91852
A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing.
96273
Is a continuous function $ f\colon(0,\infty)\to R$, such that $f(x)\leq f(nx)$ increasing?
117502
Proving that a certain continuous function is surjective.
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
77943
If $f$ is continuous, then there exists $x+\frac{1}{n}\in[0,1]$ and $f\left(x+\frac{1}{n}\right)=f(x)$