Question

Suppose f is cont. on [1,5], diff. on (1,5) and f'(x) < 3/8 for all x in (1,5). If f(1) = 1, show that f(x) < 5/2 for all x on [1,5].

Answer 1

Use the Mean Value Theorem.

Answer 2

Tried it and I failed to use it properly.

Answer 3

Let me show you my attempt.

Answer 4

I'll photocopy it, one sec.

Answer 5

Use the Mean Vaue theorom

Answer 6

I tried and I keep messing up. One sec

Answer 7

@maddog12 , @experimentX would you guys mind helping me out with this one? I have attached my attempt...

Answer 8

sure

Answer 9

Wait let me upload it so it is more clear,

Answer 10

ok

Answer 11

is this a test

Answer 12

are u allowed to use openstudy for this test

Answer 13

Shoot the bottom part got cut off. Yes this is a practice test from last term. I did not understand this question:

Yes of course, this test is already done. I am NOT

Answer 14

hahaha

Answer 15

I am NOT in the exam right now texting you abou this

Answer 16

http://i1084.photobucket.com/albums/j409/QRAWarrior/QAL.png

Answer 17

The third attempt got cut off, but it was wrong anyway. I am not sure how I am to do this

Answer 18

ok

Answer 19

Do a proof by contradiction; Assume that there's a k in [1,5] such that f(k)>=5/2. Use the MVT to derive a contradiction.

Answer 20

Do a proof by contradiction; Assume that there's a k in [1,5] such that f(k)>=5/2. Use the MVT to derive a contradiction.

Answer 21

Ok I will try. So I use f(5), f(1), 1, 5 for the MVT?

Answer 22

No, you use k, 1, f(k), and f(1).