Prove that $f'''(x) > 3$
101371
show that $f^{(3)}(c) \ge 3$ for $c\in(-1,1)$
26207
If $f$ is a quadratic and $f(x)>0\;\forall x$, and $g= f + f' + f''$, prove $g(x)>0\; \forall x$
34081
Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$
105068
Proving that the function is differentiable and $f'(0)=0$
28399
Showing $f$ is constant
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
149764
If $f$ s twice differentiable and satisfies the following constraints, prove $f'(0)>-\sqrt 2$
89429
Prove $\sup \left| f'\left( x\right) \right| ^{2}\leqslant 4\sup \left| f\left( x\right) \right| \sup \left| f''\left( x\right) \right| $
1371
Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
111458
Prove that $f$ is differentiable
105700
Proving $\,f$ is constant.
133682
Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.
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
18261
Prove $\int_{a}^{b}{f(x)dx}>0$.
33523
If $f(0)=0$ and $f'$ is increasing, then $\frac{f(x)}{x}$ is increasing.
49408
Proof of the derivative of ln(x)
13270
Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$