Question

does any one know rolles theorem?
please help

Answer 1

f(x)= 5-12x+3x^2
[1,3]
vertify that function staifies the three hyp of rooles thorem

Answer 2

check that \(f(1)=f(3)\) first

Answer 3

since it is a polynomial, it satisfies all the other parts of the hypothesis
namely:
it is differentiable on \((1,3)\) and it is continuous on \([1,3]\)
it must be, since it is a polynomial

Answer 4

of all those conditions are met, the the conclusion is there is a number \(c\in (a,b)\) with
\[f'(c)=0\]

Answer 5

*if

Answer 6

in fact, since you have a quadratic, not only does \(c\) exist, but it must be right in the center of \((1,3)\) i.e. \(c=2\)

Answer 7

why c is 2?

Answer 8

did you check that \(f(1)=f(3)\)?

Answer 9

yes i got this one too. but its 3 not 2..?

Answer 10

i just did and i got \(-4\) for both

Answer 11

now take the derivative, set it equal to zero and solve
i bet you get \(2\)

Answer 12

it has to be if you have a quadratic

Answer 13

in general the solution does not have to be in the center of the interval, but it does if you have a quadratic
in any case for this one you get
\[-12+6x=0\] and so \(x=2\)

Answer 14

O i got it thank you!
its not about math question..but
do you know how to minimize the screen?
this webpage is way too big all of sudden

Answer 15

no idea
i just go to the top and minimize

Answer 16

it worked. thank you!!!