Question

Someone help me Please! (:
Let f(x)=2sin(x)

1.) |f'(x)| is less than or equal to _____.
2.) By the Mean Value Theorem, |f(a)-f(b)| is less than or equal to _____. |a-b| for all a and b.

Answer 1

First, what is f'(x)?

Answer 2

f'(x)=2cos(x)

Answer 3

Now, the |a| stand for the absolute value of a.
2cos(x) is a wave with what amplitude? You can type y = 2*cos(x) in Google for a graph of it :)

Answer 4

it would be 2 right?

Answer 5

Yes it would :) 2 is the magnitude of the function.
Now, do you know the mean value theorem, or can you find it in your book?

Answer 6

@pdd21 Have you answered 1.) yet?

Answer 7

yes!(: @genius12

Answer 8

\[\frac{ f(b)-f(a) }{ b-a }\] @TimSmit

Answer 9

@pdd21 what did you get for 1.)?

Answer 10

Well the final conclusion for 1. should be drawn indeed, thanks genius12, I have to go in a minute however and I was the only one replying :)

Answer 11

i got \[\left| f \prime(x) \right|\le 2\] @genius12

Answer 12

@pdd21 That is the theorem indeed, however a part is missing I believe. What is the equality/inequality?

Answer 13

equality/inequality?

Answer 14

oh wait it would be 2. because the point/interval is [0,2] right?

Answer 15

and you evaluate it by the MVT.

Answer 16

We're at question 2 now right?

Answer 17

yeah I was able to solve #2.(:
thank you for all the help though! I really appreciate it! @TimSmit

Answer 18

Ok, my help wasn't needed at the harder part it seems then :p No problem, good luck with the studying!

Answer 19

@pdd21 for number, what are we trying to fill the blank in with?