Show that $f$ differentiable implies $f$ continous
43874
Differentiability implies continuity - A question about the proof
54729
Prove that $f$ has a fixed point .
151573
Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
145368
How to show $f:Y\to X^{+}$ is continuous?
158681
How to show that $e^x$ is differentiable?
58664
Proving a function is continuous for a fixed variable
69378
The derivative of $x!$ and its continuity
117906
Show that $\liminf\limits_{x\to \infty}|f'(x)|=0$ if $\lim\limits_{x\to \infty}f(x)/x=0$ and $f$ is differentiable
126461
Show that $g:I\to\mathbb{R}$ is continuous and $f:(x-x_0)g(x)$ is differentiable
145173
$f: \mathbb{R}^2-\{0\} \rightarrow \mathbb{R}$ is continuously differentiable and $f(\alpha x) = \alpha^2f(x)$, then $x \cdot \nabla f(x) = 2 f(x)$
104263
How to show that $f'(x)<2f(x)$
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
150005
Existence of points in a differentiable function
105652
Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
144013
If $f$ is differentiable at $x = x_0$ then $f$ is continuous at $x = x_0$.
93528
Continuous versus differentiable
17223
Continuity of an inverse function.