How can I show that if a twice continuously differentiable function f:R->R and its second derivative f'' are bounded, the first derivative f' must also be bounded?
It's easy to imagine, but how to prove?
Thank you for your help!
How can I show that if a twice continuously differentiable function f:R->R and its second derivative f'' are bounded, the first derivative f' must also be bounded?
It's easy to imagine, but how to prove?
...if a twice continuously differentiable function f:R->R and its second derivative f'' are bounded...
I could be misreading (or misunderstanding) things, but I think both the original function f(x) and also the second derivative are to be bounded. I don't think a quadratic would qualify.What about \(\displaystyle f(x)=x^2+x+1~?\)
What is the definition of a bounded function?
I could be misreading (or misunderstanding) things, but I think both the original function f(x) and also the second derivative are to be bounded. I don't think a quadratic would qualify.
Can you use something similar to #19 here?
The above comment is in reference to work assigned to a fourth year/first year graduate course at Georgia Tech.Thank you, this is a great approach!