Mean value theorem for the second derivative, when the first derivative is zero at endpoints
34081
Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$
24478
What is the name of this theorem, and are there any caveats?
5371
If a function has a finite limit at infinity, does that imply its derivative goes to zero?
53767
How to prove that derivatives have the Intermediate Value Property
39451
Proving inequation with maximum and 2nd derivative
131444
Local maximum implies derivative is $0$
109943
Estimates of the value of a holomorphic function and its derivative
107894
Inequality involving the sup of a function and its first and second derivatives
12556
A non-trivial, non-negative, function bounded below by its derivative with $f(0)=0$?
48920
Mean value theorem for integrals: how does the sign matter?
117595
Minimum Modulus Principle for a constant fuction in a simple closed curve
128719
Are constants the only continuous functions with "symmetric derivative" zero?
88080
Applying MVT to function that has limit of its derivative given when $x\to\infty$
20117
Mean curvature in asymptotic directions
39674
Rolle's Theorem and the Mean Value Theorem
48476
Mean value theorem rolle's theorem
134382
Proving bounded first derivative