Thread: Intermediate Value theorem, zero between 2 and 3

Use the intermediate value theorem to show that f(x) = -x^4 + 3x^3 - 2x + 1 has zero between 2 and 3

I did
a=2, b=3

so

f(a) = -(2)^4 + 3(2)^3 - 2(2) + 1
= -16 + 24 - 4 + 1
= -20 + 25
= 5

f(b) = -(3)^4 + 3(3)^3 - 2(3) + 1
= - 81 + 81 - 6 + 1
= -87 + 82
= -5

Is this correct?

Originally Posted by mwok

Use the intermediate value theorem to show that f(x) = -x^4 + 3x^3 - 2x + 1 has zero between 2 and 3
a=2, b=3 so
f(a) = 5 & f(b) = -5
Is this correct?

Yes the calculutions at correct. But so what?
You need to explain what all that proves and why?

Originally Posted by Plato

Yes the calculutions at correct. But so what?
You need to explain what all that proves and why?

Hint to Plato: is this function continuous? Why? Notice that the Intermediate Value Theorem can finish your proof instantly, given that f(x) is satisfies its hypotesis.

Regards,

Originally Posted by Plato

Yes the calculutions at correct. But so what?
You need to explain what all that proves and why?

Well, both 2 and 3 does NOT produce the zeroes...it produces 5 and -5 but the question is stated in a way that it DOES produce zeroes......how?

Originally Posted by mwok

Well, both 2 and 3 does NOT produce the zeroes...it produces 5 and -5 but the question is stated in a way that it DOES produce zeroes......how?

The point is that because one is negative the other positive then by the intermediate value theorem, zero being between then, must be a functional value of a continuous function.

Originally Posted by Rafael Almeida

Hint to Plato: is this function continuous? Why? Notice that the Intermediate Value Theorem can finish your proof instantly, given that f(x) is satisfies its hypotesis.

Rafael Almeida, with all due respect, I don’t think that you have the experience to correct me. What I clearly was trying to do was to guide the poster to an understanding of his/her own

Rafael Almeida, with all due respect, I don’t think that you have the experience to correct me. What I clearly was trying to do was to guide the poster to an understanding of his/her own

Dear Plato,

I am sorry, I never meant to. Now I see what happened, I mistook your username for mwok's. I though the username Plato started the topic.

To clarify things, the tip was to mwok. And surely, I don't have neither the experience nor the reputation to correct anybody in here, particularly a poster like you. I'm more a learner than a tutor and I hope to help where I can while I work out my learning process with the help of people like you.

So, again, sorry for the misunderstanding.

Sincerely,

Ah, I get it now. Thanks guys!