Analysis: Show that there exists an $x$ so that $f'(x)=0$. (Derivative at point is equal to$ 0$)
136980
Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
16375
Is the function differentiable at $0$?
113343
$f$ is constant if derivative equals zero
105068
Proving that the function is differentiable and $f'(0)=0$
13150
If the derivative of $f$ is never zero, then $f$ is one-to-one
39995
Showing that partial derivatives of $f(x) = \frac{xy}{x^2+y^2}$ exist for $(x,y) \neq (0,0)$
4636
How to show that $f$ is differentiable at $x=0.$
109561
Find $F'(x)$ if $F(x) = \displaystyle \int_{0}^x xf(t)dt$.
101778
Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
143874
Limit of derivative is zero. Does it imply a limit for f(x)?
13202
Prove that there exists at least one $x_0\in\mathbb{R}$, such that $f(x_0)+f''(x_0)=0$
112923
Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
69378
The derivative of $x!$ and its continuity
85739
Show that $f(x) = 0$ for all $x \in [a,b]$ given $|f'(x)| \leq C|f(x)| $