Question

let f(x)=sqrt(2x-x^2)

Answer 1

on the interval [0,2]. find all numbers c that satisfy the mean value thereom on the interval

Answer 2

Evaluate the end points, find the gradient between those point.
Then differentiate f(x) and equate this to the gradient found above. Solve for x.

Answer 3

what do you mean?

Answer 4

Do you know what the mean value theorem is?

Answer 5

yes

Answer 6

Okay, so you understand you must first find the gradient between the two end points (0, f(0)) and (2, f(2))?

Answer 7

dont' get your terminology when you say gradient

Answer 8

the slope of the line joining those two points

Answer 9

so are you trying to say plug the endpoints into the formula??

Answer 10

yes ... i really dont know how you dont understand this if youre at a level where youre using the MVT

Answer 11

my teacher never used that terminology...

Answer 12

what nationality are you?

Answer 13

american

Answer 14

Okay. So we can get on a level playing field, please explain to me your understanding of the MVT. I will then help you using your syntax.

Answer 15

i know that you can have multiple c after plugging in your interval numbers and those c's are critical points???

Answer 16

once i get f'(c) do i then set it equal to 0??

Answer 17

Okay, you don't understand MVT.
http://en.wikipedia.org/wiki/Mean_value_theorem
Try reading that. The graph should be helpful. Let me know if you don't understand certain parts.

Answer 18

thanks

Answer 19

i solved the problem... first i had to get the derivative, then plug my values into the mvt formula and then once i got the f'(c) i then plugged that into my solution of the derivative and got a c value... that value is 2

Answer 20

Your method sounds about right, but the answer isnt, unfortunately. Feel free to show your working if you want me to stop the mistake.

Answer 21

i see my mistake

Answer 22

there seems to be an issue because... when i plug in the f'c value into the derivative it's indeterminate