1. ## rolle's theorem

for g(x)=x^3 + 3x^2 -2, show that there must ne one real root on [0,2]

2. Originally Posted by wisezeta
for g(x)=x^3 + 3x^2 -2, show that there must ne one real root on [0,2]
try instead the Intermediate Value Theorem.

3. Originally Posted by skeeter
try instead the Intermediate Value Theorem.
can u do it using rolle's theorem?

4. Originally Posted by airportman92
can u do it using rolle's theorem?
Rolle's theorem says that if a function is continuous on [a,b], differentiable on (a,b), and f(a) = f(b) , then there is at least one value c in the interval (a,b) where f'(c) = 0.

I'm not saying it can't be done, but it would not be as simple as using the IVT.

5. Originally Posted by skeeter
Rolle's theorem says that if a function is continuous on [a,b], differentiable on (a,b), and f(a) = f(b) , then there is at least one value c in the interval (a,b) where f'(c) = 0.

I'm not saying it can't be done, but it would not be as simple as using the IVT.

how would you do it using rolle's theorem though just for fun

6. Originally Posted by airportman92
how would you do it using rolle's theorem though just for fun
it would not be fun.

7. Originally Posted by skeeter
it would not be fun.
but how do u do it hah

8. Originally Posted by airportman92
but how do u do it hah
I'm not sure.

9. someone how do you use rolles theorem to do this one lol

10. It's a useless detour (at least how I did it is), but since you want it so badly:

Let $g_c(x)= \frac{x^4}{4} + x^3 -2x +c=4x(x^3+4x^2-2)+c$ Let $h(x)=x^3+4x^2-2$ then $h(0)<0$ and $h(2)>0$ so by the intermediate value theorem there exists $d\in (0,2)$ such that $h(d)=0$ and so $g_c(0)=g_c(d)=c$ and by Rolle's theorem there exists $y\in(0,d)$ such that $g'_c (y)=0$ but $g'_c=g$

As skeeter said, not pretty at all.
The text passage is a discussion thread where users are asking and answering a question about using Rolle's theorem to show that a function has a real root on a given interval. The main question is whether the problem can be solved using Rolle's theorem, and there is a provided solution using this theorem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
1. ## rolle's theorem

for g(x)=x^3 + 3x^2 -2, show that there must ne one real root on [0,2]

2. Originally Posted by wisezeta
for g(x)=x^3 + 3x^2 -2, show that there must ne one real root on [0,2]
try instead the Intermediate Value Theorem.

3. Originally Posted by skeeter
try instead the Intermediate Value Theorem.
can u do it using rolle's theorem?

4. Originally Posted by airportman92
can u do it using rolle's theorem?
Rolle's theorem says that if a function is continuous on [a,b], differentiable on (a,b), and f(a) = f(b) , then there is at least one value c in the interval (a,b) where f'(c) = 0.

I'm not saying it can't be done, but it would not be as simple as using the IVT.

5. Originally Posted by skeeter
Rolle's theorem says that if a function is continuous on [a,b], differentiable on (a,b), and f(a) = f(b) , then there is at least one value c in the interval (a,b) where f'(c) = 0.

I'm not saying it can't be done, but it would not be as simple as using the IVT.

how would you do it using rolle's theorem though just for fun

6. Originally Posted by airportman92
how would you do it using rolle's theorem though just for fun
it would not be fun.

7. Originally Posted by skeeter
it would not be fun.
but how do u do it hah

8. Originally Posted by airportman92
but how do u do it hah
I'm not sure.

9. someone how do you use rolles theorem to do this one lol

10. It's a useless detour (at least how I did it is), but since you want it so badly:

Let $g_c(x)= \frac{x^4}{4} + x^3 -2x +c=4x(x^3+4x^2-2)+c$ Let $h(x)=x^3+4x^2-2$ then $h(0)<0$ and $h(2)>0$ so by the intermediate value theorem there exists $d\in (0,2)$ such that $h(d)=0$ and so $g_c(0)=g_c(d)=c$ and by Rolle's theorem there exists $y\in(0,d)$ such that $g'_c (y)=0$ but $g'_c=g$

As skeeter said, not pretty at all.
user
The text passage is a discussion thread where users are asking and answering a question about using Rolle's theorem to show that a function has a real root on a given interval. The main question is whether the problem can be solved using Rolle's theorem, and there is a provided solution using this theorem.

TYPE: SINGLE_QUESTION_WITH_ANSWER