Please Help - Calculus Question

Question

Give an example of, and explain why the example is sufficient for the following:

1. Functions f and g with f’(x) = g’(x), ∀x, but f(x) ≠ g(x)
2. A function f(x) such that f’’(x) = –f(x)
3. Function with a critical point but no local minimum or maximum
4. A function with an absolute minimum at x = c, for which f’(c) does not exist
5. A function that is concave down on (0,1) with no local extreme on (0,1)

Answer 1

I will answer 4/5 for you...you work on the last one.

1. f(x)=g(x)+C
2. Not real valued function but f(x)=e^ix + e^-ix works.
3. Look at x³ at x=0
4. If c is the end point of a closed interval on which f is defiend.