Use the intermediate value theorem to show that f has a zero between a and b.

$$f(x)=2x^3+5x^2-3$$ where a=-3 and b=-2.

Question

Use the intermediate value theorem to show that f has a zero between a and b.

$$f(x)=2x^3+5x^2-3$$ where a=-3 and b=-2.

anonymous · Answer

My question is how do you use the intermediate value theorem when f is not a polynomial?

zarkon · Answer

but your $f$ is a polynomial

zarkon · Answer

to use the IVT you just need a continuous function

anonymous · Answer

It doesn't have x^1

zarkon · Answer

sure it does...$$0x^1$$

anonymous · Answer

Oh... haha okay... how would it look if the function is not continuous?

zarkon · Answer

if it is a polynomial then is is always continuous

anonymous · Answer

Hmm, okay :).

anonymous · Answer

@Zarkon  so why do we have to test?

zarkon · Answer

test?

anonymous · Answer

if we know it's continuous and there exist a zero? It's just a method of proof?

zarkon · Answer

no...it can also be used to numerically find the zero.

zarkon · Answer

anonymous · Answer

Oh, Okay :). Thanks!!!