How do we determine if $f '(0)$ exists
21879
Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
118195
How does one prove that $e$ exists?
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
77331
$f$ function with $\nabla f=\bar{0}$
39921
show that f is constant on I
104263
How to show that $f'(x)<2f(x)$
5371
If a function has a finite limit at infinity, does that imply its derivative goes to zero?
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
154612
$\int_{0}^{x} f(t) dt \ge {f(x)}$ holds or not on $[0,1]$
76311
$f'' + f =0$: finding $f$ using power series
99827
For what values will f(x) be necessarily one-one?
153510
Questions about the existence of a function
83907
$f$ bounded but $f'$ isn't
135577
Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
113888
Behavior of derivative near the zero of a function.
87041
How to determine with certainty that a function has no elementary antiderivative?
105790
What is the Fourier Transform of $f'(x)/x$