Question

Show that the equation has a root in the given interval. F(x)=-x^4+3x^2+5=0 What the heck are they asking me to do here???

Answer 1

whts the interval?

Answer 2

integrate this eqn

Answer 3

then put inh both the boundary values of the interval [a,b]
the values obtained will be same for a and b

Answer 4

oh sorry, interval is 2,3

Answer 5

so integrate ur eqwn and then put in 2 and 3..ull c the values obtained at 2 and 3 are equal
hence proved

Answer 6

so I am using 2 and just plugging it in, and then do the same with 3?

Answer 7

after integrating the eqn..yes

Answer 8

does F symbolize the the antiderivative

Answer 9

@ssnapier:

Are you in a calculus class?

Answer 10

not necessary@myininaya

Answer 11

this is for college algebra

Answer 12

if F symbolizes the function we are trying to find a root,
we just evaluate F at 2 and evaluate F at 3
if one is positive and one is negative, then we have a root on that interval

Answer 13

Ah ok. Ignore the part about integrals then. That's like 2 years ahead of what we're dealing with. :P

Answer 14

yeah...we can do that as well....i ws applying the rolles thm

Answer 15

to apply rolle's thm the continous F must satify F(2)=F(3),
then do F'(c)=0 and solve for c

Answer 16

@him: you have to remember he's in college algebra. He hasn't even begun touching limits let alone derivatives and integrals and antiderivatives. There's gotta be an alternate way to do this (I just can't remember it).

Answer 17

all you do is do F(3) and F(2) ;lol

Answer 18

I am doing it right now...

Answer 19

ummmm, I must have done this wrong...

Answer 20

@uber: how cn i guess wht level hes studying
@ssnapier : sorry mate

Answer 21

I plugged in 2, and got 16+12+5=0 how can that be??

with 3 I got 81+27+5=0

Answer 22

F(2)=1
F(3)=-49

Answer 23

uve got a minus at the beginning i suppose..yeah shes right..

Answer 24

holy hell... how did I ge that far off??

Answer 25

but -2^4 is a positive 16, right?

Answer 26

u ignored the minus sign at the beginning

Answer 27

its -(x^4)

Answer 28

the negative is not being raised just the x

Answer 29

ahhhhh, that makes much more sense...

Answer 30

since F(2)>0 and F(3)<0, then there is a number between 2 and 3 lets call it c such that F(c)=0

Answer 31

bingo

Answer 32

I can't believe that such a simple concept actually was accredited to someone. lulz.

Answer 33

maybe it wasn't so easy to see back then

Answer 34

Then again... I disagree with the theorem. What if there's a hole at where y would equal zero? I mean I know it doesn't have a hole here because we've got a polynomial, but what if it was something like "in the interval 3,5... prove that -blahblah/(x-4) has a zero"

At 4, it'd die. And I'd make the equation purposely have a limit approaching zero at 4 :P

Answer 35

the function has to be continuous

Answer 36

intermediate value theroem

Answer 37

Then I'll fall back to my previous point. :P
As long as Cartesius hadn't invented his graphing system yet, there's no reason for anyone to be surprised by this logic.

But if it was before the graph was invented, then this guy deserves his credits. :D

Answer 38

to apply any theorems it must also satisfy the hypothesis of that theorem