Use mean value theorem to find $f(\xi)+f''(\xi)=0$
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
19845
Mean Value Theorem for Integrals
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
73240
How do I prove this form of mean value theorem for integral?
13202
Prove that there exists at least one $x_0\in\mathbb{R}$, such that $f(x_0)+f''(x_0)=0$
4064
An equality involving the mean value property
158520
Derivative of Fourier transform: $F[f]'=F[-ixf(x)]$
152293
Solution of $y''+xy=0$
100765
If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
70621
Question concerning the mean-value property
104263
How to show that $f'(x)<2f(x)$
67738
Mean Value theorem problem?(inequality)
67364
If $\lim_{x\to\infty}(f(x)+f'(x))=L$ show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$
11707
If $x\sqrt{1+y}+y\sqrt{1+x}=0$ find $y'$
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
39674
Rolle's Theorem and the Mean Value Theorem
128495
Integral Inequality $|f''(x)/f(x)|$