Show that if $f'$ is strictly increasing, then every tangent line to the graph $y = f(x)$ intersects it exactly once
136204
Intersection of a function having increasing derivative with tangent line
31548
Proof of "every convex function is continuous"
116851
Show that f(x) is convex
145368
How to show $f:Y\to X^{+}$ is continuous?
123976
Slope of the tangent line, Calculus
157939
prove that a graph is one-ended
110691
Proving that given any two points in a connected manifold, there exists a diffeomorphism taking one to the other
102764
Let $f(x)=\int_0^1|t-x|t~dt$ for all real $x$. Sketch the graph of $f(x)$, what is the minimum value of $f(x)$
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
105658
Show that a function that is locally increasing is increasing?
5295
Can the graph of a bounded function ever have an unbounded derivative?
48764
Increasing real valued function whose image set is connected
84021
How can we show that $\varphi(a) \neq a +1$ for every $a \in A$?
102598
Show that $X$ is path connected if and only if each $X_\alpha$ is path connected.
150699
Show that if $f'$ is strictly increasing, then $\frac{f(x)}{x}$ is increasing over $(0,\infty)$
23294
Show that the function $f = \frac{xy}{x^2 + y^2}$ is continuous along every horizontal and every vertical line
153767
Singular points and tangent lines