Rolles Theorem

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• Apr 1st 2010, 07:33 AM
sderosa518
Rolles Theorem
Determine if the Rolles theorem can be applied. If it applies find "c" such that f(x)=(x-2)(x+3)^2, [-3,2]
• Apr 1st 2010, 07:37 AM
Ted
Quote:

Originally Posted by sderosa518
Determine if the Rolles theorem can be applied. If it applies find "c" such that f(x)=(x-2)(x+3)^2, [-3,2]

f is differentiable and continuous since its a polynomial function
and $f(-3)=f(2)$
so the rolle's theorem can be applied here

I do not know what do you mean with:

Quote:

Originally Posted by sderosa518
find "c" such that f(x)=(x-2)(x+3)^2, [-3,2]

I think you mean find "c" that satisfies the rolle's theorem, right?
• Apr 1st 2010, 07:45 AM
sderosa518
Yes!!!
• Apr 1st 2010, 07:56 AM
Ted
Quote:

Originally Posted by sderosa518
Yes!!!

you want to solve $f'(c)=0$ for c ..
so ?
• Apr 1st 2010, 08:20 AM
sderosa518
This is what I got. I use the product rule to solve.

3x^2+8x-3

Not sure if I am right or not
• Apr 1st 2010, 08:44 AM
Ted
Quote:

Originally Posted by sderosa518
This is what I got. I use the product rule to solve.

3x^2+8x-3

Not sure if I am right or not

correct
so $f'(x)=3x^2+8x-3$
hence $f'(c)=3c^2+8c-3$
$f'(c)=0 \rightarrow 3c^2+8c-3=0$
now solve the last equation for c
• Apr 1st 2010, 08:52 AM
sderosa518
Any hint on how to solve it?

Should I factor a 3 out or factoriztion (x-1)(x+1)
or just simply solve for zero
• Apr 1st 2010, 09:27 AM
Ted
Quote:

Originally Posted by sderosa518
Any hint on how to solve it?

Should I factor a 3 out or factoriztion (x-1)(x+1)
or just simply solve for zero

you should know how to solve it
• Apr 1st 2010, 10:21 AM
sderosa518

Correct???
• Apr 1st 2010, 10:26 AM
Ted
wrong
you should get -3 and 1/3
• Apr 1st 2010, 11:15 AM
sderosa518
Curious how did you get?

• Apr 1st 2010, 11:26 AM
Ted
Quote:

Originally Posted by sderosa518
Curious how did you get?

I will be happy if i see your complete work
• Apr 1st 2010, 11:34 AM
sderosa518
F(x)= 3x^2+8x-3

-8 -+Sqrt(8^2-4(3)(-3))
------------------------
2(3)

-8 +-sqrt(100)
--------------
6

-8+-10
------- = 2, -14/3
6

Do you see where I got my answer. When you or if you show mean, I am going to feel stupid!??!
• Apr 1st 2010, 12:24 PM
Ted
Quote:

Originally Posted by sderosa518
F(x)= 3x^2+8x-3

-8 -+Sqrt(8^2-4(3)(-3))
------------------------
2(3)

-8 +-sqrt(100)
--------------
6

-8+-10
------- = 2, -14/3
6

Do you see where I got my answer. When you or if you show mean, I am going to feel stupid!??!

$\frac{-8-10}{6}$ and $\frac{-8+10}{6}$