Thread: 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(b-a)

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))/(b-a)=f'(c)>=M

so

f(b)-f(a)>=M(b-a)

f(b)>=f(a)+M(b-a)

Can you explain that to me? Please =)

The MVT says that

(f(b)-f(a))/(b-a)=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))/(b-a)=f'(c)>=M

multiply both sides by (b-a)

f(b)-f(a)>=M(b-a)

add f(a) to both sides

f(b)>=f(a)+M(b-a)

Thanks bro!