In: Math
Let f(x) be differentiable on the interval [a,b]. Select all of the following statements which must be true.
1. f(x) must attain its maximum value on the interval [a,b]
2. There is some number c in the interval (a,b) such that f′(c)= (f(b)−f(a))/ (b−a)
3. f(x) is integrable on [a,b].
4. f(x) is continuous on (a,b).
5. f(x) is a polynomial.
6. f(x) is an increasing function.