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

$$f(x)=x^5+x^3+x^2+x+1$$
where $$a=-\frac{1}{2}$$ and $$b=-1$$.

Question

Use the intermediate value theorem to show that f has a zero between a and b.

$$f(x)=x^5+x^3+x^2+x+1$$
 where $$a=-\frac{1}{2}$$ and $$b=-1$$.

anonymous · Answer

First, in order to use the intermediate value theorem, we have to identify the function as being continuous, (which this one is, because it is a polynomial.)

Find:$$f(a)$$ and $$f(b)$$ and as long as you can fit a zero between the two you're done!

anonymous · Answer

@michealwwells  But doesn't a have to be <b

anonymous · Answer

@purplec b could be the larger of the two, the idea is that there is something between the two.  The theorem states that if the function is continuous, and we can find two values within it, there must be something between them.  In this example we are trying to see if there is a zero between them, but it doesn't matter who is bigger (a or b) as long as zero fits between f(a) & f(b).  I hope that makes some sense.

anonymous · Answer

Yes it does... Thank you :). I don't know why they state for a<b if that is not going to be so for every question to confuse me :(.