Show that if $f$ is a differentiable function whose third derivative is continuous, then there exists $c\in (0,1)$ such that $f'''(c)\geq 24$
96224
Given second and first derivatives at 2 points, prove that some point in between them has third derivative greater than or equal to 24.
105999
An application of derivatives problem- to show that $f(x+2)-f(x)>2$ for $f(x)=x\cos(1/x)$
99906
If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$
38923
What can we say about differentiability of $f$ at $c$?
104263
How to show that $f'(x)<2f(x)$
17223
Continuity of an inverse function.
105084
Let f be a function twice differentiable and with derivatives continuous on an interval $[a,b]$ containing $0$. Prove the following statement:
151410
Inequality of continuous functions
115635
Differentiability of antiderivative and continuity of derivative
143174
property of continuous function
150554
proof that $f'$ is continuous at $a$
149764
If $f$ s twice differentiable and satisfies the following constraints, prove $f'(0)>-\sqrt 2$
53726
Prove that if $f$ is a real continuous function such that $|f|\le 1$ then $|\int_{|z|=1} f(z)dz| \le 4$
122330
Prove that there exists some $c\in(-3,3)$ such that$ \ \ g(c) \cdot g''(c)<0$.
138864
If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f(x+y)=f(x)f(y)$ and $f'(0)$ exists, then $f$ is differentiable on $\mathbb R$
154881
Question on differentiability of a continuous function
84436
third derivative of inverse function