Is it true that f is differentiable, and $\lim_{x\to\infty}f(x)=0,$ then $\lim_{x\to\infty} f'(x)=0$
5371
If a function has a finite limit at infinity, does that imply its derivative goes to zero?
23222
If $f(x) + f'(x) + f''(x) \to A$ as $x \to \infty$, then show that $f(x) \to A$ as $x \to \infty$
19986
How can this be proved $\lim_{x\to\infty}(f(x)+f'(x))=l$
111470
Proof of differentiability of $f(x)$
49705
Is $f(x,y)=(x+2y+y^2+|xy|, 2x+y+x^2+|xy|)$ differentiable?
10428
Proving that $\lim\limits_{x\to\infty}f'(x) = 0$ when $\lim\limits_{x\to\infty}f(x)$ and $\lim\limits_{x\to\infty}f'(x)$ exist
111290
If $f$ continuous and $\lim_{x\to-\infty }f(x)=\lim_{x\to\infty }f(x)=+\infty $ then $f$ takes its minimum.
49511
Do we have $\lim_{h\to 0^+}\int_0^\infty|f(t+h)-f(t)|dt=0$?
129579
If $f''(x_0)$ exists then $\lim_{x \to x_0} \frac{f(x_0+h)-2f(x_0)+f(x_0-h)}{h^2} = f''(x_0)$
144422
How to prove that $\lim\limits_{x\to\infty} f(x)/x=L$
105068
Proving that the function is differentiable and $f'(0)=0$
148737
Is $|xy|$ differentiable in $(0,0)$?
44060
If $\lim_{x \to +\infty} f'(x) = L$, then $\lim_{x \to \infty} \frac {f(x)}{x} = L$
28949
Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$
117338
Counterexample to second derivative test when f''(x) is not continuously differentiable
68156
For a differentiable function $f:\mathbb{R} \rightarrow \mathbb{R}$ what does $\lim_{x\rightarrow +\infty} f'(x)=1$ imply? (TIFR GS $2014$)
68752
A few questions about infinite derivative.