Verify that the function satisfies the hypothesis of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of the MVT. f(x) = x/x+2 [1,4]

Question

Verify that the function satisfies the hypothesis of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of the MVT. f(x) = x/x+2    [1,4]

amistre64 · Answer

the function goes bad at -2; so the interval itself is fine

amistre64 · Answer

as long as there as a slope from end to slope we should be able to satisfy the MVT

amistre64 · Answer

slope from end to end ....

amistre64 · Answer

f(1)=1/3
f(4)=4/6 = 2/3

f(x) moves 1/3, as x moves 3

1/3
--- = 1/6 for a slope
  3

amistre64 · Answer

as long as the derivative of the interval has points that match 1/6; we are good

amistre64 · Answer

f(x) = x/x+2
f'(x) = 2 /(x+2) ^2 = 1/6 when (x+2)^2 = 12

amistre64 · Answer

as long as -2+2sqrt(3) is in the interval, wes good

amistre64 · Answer

1.464...

looks good

anonymous · Answer

okay cuz i had a problem wit the derivative

anonymous · Answer

thank you

amistre64 · Answer

yep