Prove $[f'(x)]^2<2f(x)$ for any $x$.
71857
Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $
110093
Proving that the solution to $f^{\prime}(x) = \frac{1}{x^{2} + (f(x))^{2}}$ is bounded above.
63526
Proving that $(\sup_{x\in R}|f'(x)|)^2\leq 4\sup_{x\in R}|f(x)|\cdot\sup_{x\in R}|f''(x)|$.
64437
Proof by induction (power rule of the derivative)
18261
Prove $\int_{a}^{b}{f(x)dx}>0$.
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
9270
Differentiable function, with $f'(x)=[f(x)]^2$
98255
Find $f(x)$ such that $f(f(x)) = x^2 - 2$
49408
Proof of the derivative of ln(x)
116056
Prove that $|f(x)-f(y)|\le|x-y|$ for all $x$ and $y$.
16418
Showing that $\frac{f(x)-f(x-h)}{h} \le f'(x) \le \frac{f(x+h)-f(x)}{h}$ given that f' is increasing
150699
Show that if $f'$ is strictly increasing, then $\frac{f(x)}{x}$ is increasing over $(0,\infty)$
128790
Prove an integral inequality: $ \left(\int|f|^2dx\right)^2\le 4\left(\int|xf(x)|^2dx\right)\left(\int|f'|^2dx\right) $
78319
Show that $x \mapsto \frac{f(x)}{x}$ is strictly increasing on (0,1) given that f '(x) is strictly increasing on (0,1) and that f(0)=0
135577
Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
139111
Prove that $a<c<b$, $\frac{f(b)-f(a)-(b-a)f'(a)}{g(b)-g(a)-(b-a)g'(a)}=\frac{f"(c)}{g"(c)}$
97558
Prove that $\left| f'(x)\right| \leq \sqrt{2AC}$ using integration