Find function f(x) Find function f(x), where:
$$f(3)=3$$
$$f'(3)=3$$
$$f'(4)=4$$
$$f''(3) = \nexists$$ 
How to find function like this in general? What steps should I do?

Take a function $|x|$ which has no derivative at 0. Integrate it to get a function $x\cdot|x|$ (yes, $1\over2$ is missing, but who cares) which has no second derivative at 0. Shift it to get $(x-3)|x-3|$ which has no second derivative at 3. Add some $const\cdot x^2$ to get $f'(4)-f'(3)=1$. Then add some $const\cdot x$ to get whatever derivative you like at 3. Then add a constant to get the desired value at 3.
