Question

HELP I WILL MEDAL AND FAN!

Answer 1

What's your question?

Answer 2

You are having a conference call with the CEO of a paper company. You have interpreted the number of trees cut down versus profit as the function P(x) = –x4 + x3 + 7x2 − x − 6. Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. Use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0).

Answer 3

One minute, I will graph the function.

Answer 4

Thank you so much

Answer 5

is it x^4?

Answer 6

Then x^3?

Answer 7

\[x ^{3}\]

Answer 8

Like that?

Answer 9

yea

Answer 10

Ok.

Answer 11

Here is the function.

Answer 12

p(x)=0 at the points of x=-2, -1, 1, 3

Answer 13

How would i explain this to a CEO? And thank you so much

Answer 14

It's highest point is (2.25, 12.95)

Answer 15

Lowest is (0.07, -6.04)

Answer 16

Not a problem. I will write that in a second.

Answer 17

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

Answer 18

Our leading coefficient is \[-x ^{4}\]

Answer 19

That's what you would say?

Answer 20

Not precise, but I would mention of how leading coefficients and their exponents deal with the end behavior. I was just putting that there so you knew what it meant. In this case, we have an even exponent, but a negative leading coefficient. This means each end of the graph will be opening down. (Which that was

Answer 21

proven in our graph.)

Answer 22

Is this Algebra or Calc?

Answer 23

Alg

Answer 24

Okay. Then we won't mention of max or min local/aboslute extrema.

Answer 25

You are having a conference call with the CEO of a paper company. You have interpreted the number of trees cut down versus profit as the function P(x) = –x4 + x3 + 7x2 − x − 6. Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. Use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0).

Example answer: We can infer from the leading coefficient of -x^4, that we will have the end behaviors of the graph opening downward , because the leading term is negative with a even degree. When we take the degree of 4, we can find the number of turns our graph will have by taking n-1=turns. So, 4-1=3, our graph will turn 3 times. Our end behaviors will be downward, because of the statement above about the leading coefficient and its degree. We can find where p(x)=0 by factoring the polynomial. p(x)=0 at the points of x=-2, x=-1, x=1, x=3. Plugging any of these options for p(x) will yield 0.

Answer 26

That's just roughly what I could think up. But, it doesn't want you graphing the equation, so you need to learn how to look at the terms within the polynomial. Graphing is good for guidance.

Answer 27

THANKS

Answer 28

eh just trying to pass high school

Answer 29

Hopefully, that all made sense. Not a problem, remember about the rule of end behaviors and your graphing days will be easy. The n-1 formula is dandy.

Answer 30

Are you in 10th or 9th?

Answer 31

11th