Question

derivative of 2 sin 8x?

Answer 1

is 2 (8 cos 8 x)?

Answer 2

Yep! Nice work. You can go ahead and simplify that to 16 cos 8x.

Answer 3

what if i want to find the average value of it on interval [-pi,pi]?

Answer 4

Are you familiar with the Mean Value Theorem?

Answer 5

no :(

Answer 6

looking it up now

Answer 7

Are you supposed to find the average value of \(f\) or of \(f'\)?

Answer 8

of f. answer is 16/pi?

Answer 9

average value formula and mean value theorem call for derivative of f anyways

Answer 10

answer is not 16/pi after all..

Answer 11

I was going to say, I've been doing this a variety of ways and keep getting an average value of zero

Answer 12

i got zero, too.

Answer 13

Pretty sure zero's the right answer :)

Answer 14

it is. what a strange-seeming answer

Answer 15

Not at all! It's perfectly intuitive. The endpoints of the interval are both 0, and it's a sine wave in between.

Answer 16

Spends the same amount of time above the axis as it does below the axis, if that makes sense.

Answer 17

ohh. ok. thank you again :-)

Answer 18

Sure thing :)