
Mean Value Theorem stuff
If anyone can help get me started on these two problems, I'd be greatful =)
1. Verify that the function satisfies the hypothesis of the Mean Value Theorem on the given interval. Then find all the numbers c that satisfy the conclusion of the given interval
f(x) = x/(x+2) on [1,4]
2. If f'(x) is greater than or equal to M on [a,b], show that f(b) is greater than or equal to f(a) + M(ba)
I am having a hard time wrapping my head around these two, so if someone could help explain how to go about looking at problems of these sorts... that'd be nice :)
Thanks guys!

2)
(f(b)f(a))/(ba)=f'(c)>=M
so
f(b)f(a)>=M(ba)
f(b)>=f(a)+M(ba)

Can you explain that to me? Please =)

The MVT says that
(f(b)f(a))/(ba)=f'(c)
for some c in (a,b)
we are given f'(x)>=M for all x in [a,b]
therefore f'(c)>=M
so...
(f(b)f(a))/(ba)=f'(c)>=M
multiply both sides by (ba)
f(b)f(a)>=M(ba)
add f(a) to both sides
f(b)>=f(a)+M(ba)
