Thread: rolle's theorem

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

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.

Originally Posted by skeeter

try instead the Intermediate Value Theorem.

can u do it using rolle's theorem?

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.

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

Originally Posted by airportman92

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

it would not be fun.

Originally Posted by skeeter

it would not be fun.

but how do u do it hah

Originally Posted by airportman92

but how do u do it hah

I'm not sure.

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

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

Let Let then and so by the intermediate value theorem there exists such that and so and by Rolle's theorem there exists such that but

As skeeter said, not pretty at all.