Second derivative test and continuity of $f''$?
117338
Counterexample to second derivative test when f''(x) is not continuously differentiable
127538
Show $f(x)=x\ln x$ is not uniformly continuous
157347
continuity, discontinuity derivative and relation to being derivative but its partials are not continuous
25482
If a function is continuous and differentiable everywhere is the derivative continuous?
66639
Second Derivative
85092
Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
53497
Prove that the function is continuous and differentiable (not as easy as it sounds imo)
105084
Let f be a function twice differentiable and with derivatives continuous on an interval $[a,b]$ containing $0$. Prove the following statement:
115712
Application of Derivatives rigorous proof
34940
Continuity of $f(x) = x^n$
150770
Why is $f^n(\xi(x))$ continuous over $x$?
111458
Prove that $f$ is differentiable
156942
Square of a second derivative is the fourth derivative
11017
Does existence of partial derivatives implies continuity at a point $(x_0,y_0)$?
158407
derivative bounded by a constant multiple of the function
125745
continuity of power series
26602
Continuity and existence of directional derivatives at all directions of a $f:\mathbb{R}^{2} \to \mathbb{R}$ given by $f(x,y)=\frac{2x^2y}{x^2+y^2}$