Question

Find the number c that satisfies the conclusion of Rolle's Theorem.
f(x) = 5 - 8x + 2x^2
[1, 3]

Answer 1

f'(x)=-8+4x
f'(x)=0 imples -8+4x=0 implies 4x=8 so x=2 since x=2 in between 1 and 3 then x=2 is the c that satisfies the conclusion of rolles thm

Answer 2

thats it??

Answer 3

Don't forget, for Rolle's theorem to be applicable, you need to show that f(1)=f(3) (which it does here).

Answer 4

and what if it doesnt

Answer 5

i assumed that was the case since it said just to look at the conclusion

Answer 6

it does...i was just wondering

Answer 7

but it easy to check to see if it does satisfy the hypothese so why not

Answer 8

Rolle's theorem is dependent upon f real being continuous on a closed interval [a,b], differentiable on the open interval, (a,b), and f(a)=f(b).

Answer 9

right vg

Answer 10

You would roll over to the mean value theorem if f(a) did not equal f(b).

Answer 11

ok i get it! thank u guys! :D

Answer 12

kk

Answer 13

but who needs rolle when u have mean value thm it easier to memorize one thm than two

Answer 14

agreed :)