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liraira [26]
3 years ago
12

Determine, using the intermediate value theorem, if the function F(x)=x^3+2x-1 has a zero on the interval [0,1]. Justify your an

swer and find the indicated zero, if it exists.
Mathematics
1 answer:
SSSSS [86.1K]3 years ago
7 0

Plug x = 0 into the function

f(x) = x^3 + 2x - 1

f(0) = 0^3 + 2(0) - 1

f(0) = -1

Note how the result is negative. The actual number itself doesn't matter. All we care about is the sign of the result.

Repeat for x = 1

f(x) = x^3 + 2x - 1

f(1) = 1^3 + 2(1) - 1

f(1) = 2

This result is positive.

---------------------------

We found that f(0) = -1 and f(1) = 2. The first output -1 is negative while the second output 2 is positive. Going from negative to positive means that, at some point, we will hit y = 0. We might have multiple instances of this happening, or just one. We don't know for sure. The only thing we do know is that there is at least one root in this interval.

To actually find this root, you'll need to use a graphing calculator because the root is some complicated decimal value. Using a graphing calculator, you should find the root to be approximately 0.4533976515

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Answer:

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Step-by-step explanation:

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5 0
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Each set of ordered pairs represents a function. Write a rule that represents the function.
malfutka [58]
My answer to the question is as follows:

First one looks like you are squaring the number, then multiplying the result by 4, i.e.

<span>y=4<span>x2

</span></span><span>second one is similar, but instead of squaring and multiplying by 4, you are squaring and then dividing by 2
</span>
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4 0
3 years ago
For their twentieth wedding anniversary, Richard and Sylvia had a party for several of their best friends. Things were going alo
kompoz [17]

Answer:

Richard is older

Step-by-step explanation:

We can set up an inequality for both statements.

Let r equal Richard's age and s equal Sylvia's age.

"I am older than my wife."

Since Richard is speaking, the inequality would look like this:

r > s

This means Richard is older than Sylvia.

"I am younger than my husband."

Since Sylvia is speaking, the inequality would look like this:

s < r

This means that Sylvia is younger than Richard.

We can flip one inequality to "see" them from the same perspective.

Let's use s < r

To make it so that we can see the relationship from Richard's perspective, flip the entire inequality.

s < r

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The inequality from the first quote is identical to this one!

Therefore, Richard is older than Sylvia.

8 0
3 years ago
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