Intermediate Value Theorem

[hsiwin3]

Use IVT to find the interval(s) of length 1/8 containing a solution of the given equation. (Select all that apply.)
f (x) = x[sup:1knarxmy]3[/sup:1knarxmy] + 2x + 1/4

[-1, 0]
[-1/4, 0]
[-1/8, 0]
[0, 1]
[7/8, 1]
[3/4, 1]

I honestly have no idea where to start. My professor didn't explain at all and there are no example problems like this in the book.

 

[daon]

I'm confused as well. The "equation" you were given is actually just a naming of the function. Its always true trivially. Second there are only two intervals of length 1/8 given. The correct answer to this question, as written, loos like the 3rd and 5th choices. You aren't asked to set f(x)=0 or anything?

 

[mmm4444bot]

We need to understand the Intermediate Value Theorem (IVT), before working any exercise based on it.

Given an interval [a, b], the IVT tells us that a zero exists between a and b if the signs of f(a) and f(b) are different.

As Loren notes, only two of the given intervals have length 1/8.

The fifth choice does not give opposite signs on f(x), so there is no zero for f between 7/8 and 1.

Check the third interval. In other words, compare the signs of f(-1/8) and f(0).