# Mean Value Theorem stuff

• Apr 10th 2007, 10:37 AM
drain
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!

• Apr 10th 2007, 01:24 PM
frenzy
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)
• Apr 10th 2007, 02:05 PM
drain
Can you explain that to me? Please =)
• Apr 10th 2007, 03:16 PM
frenzy
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)