Let f be differentiable, prove that there exists $c \in (0,1)$ such that $f(c) + f'(c) = 0 $
32506
Prove $kf(x)+f'(x)=0 $ when conditions of Rolle's theorem are satisfied .
139453
Prove that $\frac{1}{f'(a)} = \frac{1}{2\pi i} \int_C \frac{1}{f(z)-f(a)} dz$
70304
Prove there are $\xi$, $\eta$ with $f'(\xi)f'(\eta)=1$
57026
$f(0)=f'(0)=f'(1)=0$ and $f(1)=1$ implies $\max|f''|\geq 4$
85739
Show that $f(x) = 0$ for all $x \in [a,b]$ given $|f'(x)| \leq C|f(x)| $
142870
Prove the function is not differentiable at (0,0)
20273
Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.
135693
Suppose f is a twice differentiable function with $f(0)=0$ and $f(1)=1$, $f'(0)=f'(1)=0$. Then show that $|f''(x)| > 4$ for some $x$ in $(0,1)$
143491
Show that $f$ is differentiable on $(−1, 1)$.
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
13150
If the derivative of $f$ is never zero, then $f$ is one-to-one
76908
If $f'$ is differentiable at $a$ then $f'$ is continuous at $(a-\delta,a+\delta)$
99906
If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$
150005
Existence of points in a differentiable function
43874
Differentiability implies continuity - A question about the proof
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
111076
If $f$ is non-constant and entire, prove that there exists a $z_0 \in C$ such that $f(z_0)$ is a positive real number