1. ## Filling in table

Hey there, can someone help me out with this question?

Using graphing software, fill in the table below for this function f(x)= 12x3 - 5x2 - 11x + 6

What I need:

X intercepts
Degree of Polynomial
Y-int
Domain
Range
Intervals of Increase/Decrease
Local Minima/maxima
End Behavior

I know it seems kind of a lot but a lot of these should be simple but I'm stuck on a few of them. I have to complete a homework sheet about got about 10 of these to fill in, so I'm just looking to get one complete and using it as a reference point.

Here's a link for it to make it easier:

Graphing Calculator

2. real mature...

3. Originally Posted by agent2421
Hey there, can someone help me out with this question?

Using graphing software, fill in the table below for this function f(x)= 12x3 - 5x2 - 11x + 6

What I need:

X intercepts
Degree of Polynomial
Y-int
Domain
Range
Intervals of Increase/Decrease
Local Minima/maxima
End Behavior

I know it seems kind of a lot but a lot of these should be simple but I'm stuck on a few of them. I have to complete a homework sheet about got about 10 of these to fill in, so I'm just looking to get one complete and using it as a reference point.

Here's a link for it to make it easier:

Graphing Calculator

What have you done. Generally showing any willingness/attempts to do it yourself is not looked upon nicely.

I have attached the graph of f(x) if you want a better look

4. okay, what I have done for the question so far is:

x int: -1,0.8
Degree of polynomial: 3
Y-intercept: 6
Domain: xER
Range: yER
End Behavior: as x -> infinty, f (x) -> infinity,
as x --> negative infinity, f (x) --> negative infinity

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

Intervals of Increase/Decrease
Local Minima/maximua

I'm not 100% sure if the above is right but if it is then I only need to know how to do Intervals of increase/decrease and local minima/maxima...

5. I'm gald atleast all of us aren't failures like yourself... trolling a math website... you must be having a lot of fun, great education you have I bet.

6. Originally Posted by agent2421
okay, what I have done for the question so far is:

x int: -1,0.8
Degree of polynomial: 3
Y-intercept: 6
Domain: xER
Range: yER
End Behavior: as x -> infinty, f (x) -> infinity,
as x --> negative infinity, f (x) --> negative infinity

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

Intervals of Increase/Decrease
Local Minima/maximua

I'm not 100% sure if the above is right but if it is then I only need to know how to do Intervals of increase/decrease and local minima/maxima...
The second x intercept is not 0.8 although -1 is one. This means (x+1) is a factor by the factor theorem.

12x^3 - 5x^2 - 11^x + 6 = (x+1)(ax^2+bx+c)

You can find a,b and c by comparing coefficients. For example comparing the coefficients of x^3 I know that a on the right equals 12 on the left. Looking at the graph the quadratic should be a perfect square.

Intervals of increase are where f(x) is getting larger. Normally we'd use calculus to do this but if you're not familiar read it off the graph. Same with decreases and local maxima/minima

7. Originally Posted by e^(i*pi)
The second x intercept is not 0.8 although -1 is one. This means (x+1) is a factor by the factor theorem.

12x^3 - 5x^2 - 11^x + 6 = (x+1)(ax^2+bx+c)

You can find a,b and c by comparing coefficients. For example comparing the coefficients of x^3 I know that a on the right equals 12 on the left. Looking at the graph the quadratic should be a perfect square.

Intervals of increase are where f(x) is getting larger. Normally we'd use calculus to do this but if you're not familiar read it off the graph. Same with decreases and local maxima/minima
thanks for the help...

how exactly would you read it of the graph though? I don't really get the increase/decrease thing because it's a graph with infinity and going into quadrants 3/4... so can you give me an example of what it would be in this case...

Is the local maxima 8.8 by any chance ... local minima i'm not sure but is it 0.144?

8. Originally Posted by agent2421
thanks for the help...

how exactly would you read it of the graph though? I don't really get the increase/decrease thing because it's a graph with infinity and going into quadrants 3/4... so can you give me an example of what it would be in this case...

Is the local maxima 8.8 by any chance ... local minima i'm not sure but is it 0.144?
You know it's increasing up to the first point it turns and from then after it turns again. Normally we'd find the derivative, set it to 0 and voila. That's the turning point.

It is increasing from $-\infty$ to about 8.8 (a local maxima) and then from the second root of x to $\infty$

I would think the local minima would be 0 but don't quote me on it

9. okay thanks... I kind of get it.... so we only do the increases from the x axis then right? nothing below infinty should be recorded for it...

10. Originally Posted by agent2421
okay thanks... I kind of get it.... so we only do the increases from the x axis then right? nothing below infinty should be recorded for it...
No we do the increases from the below the x axis but we know that's increasing from the start of the domain because we know that's how cubics work

11. okay so what would the final answer be for this question for intervals of increase/decrease... I want to be 100% sure before I start the other questions so can you give me the answers for this one so I can see if i'm on the right track or not...

btw tahnks for the help.

12. Originally Posted by agent2421
okay so what would the final answer be for this question for intervals of increase/decrease... I want to be 100% sure before I start the other questions so can you give me the answers for this one so I can see if i'm on the right track or not...

btw tahnks for the help.
Increasing: $-\infty < x < ~ -0.9 \: \text{and} \: ~ 0.6 < x < \infty$

Decreasing: $-0.9 < x < 0.6$

My numbers are just approximate though

13. thanks for your time... one last question... where did you get the -0.9 from...

14. f(-0.9) ~ 8.8 which is the local maximum

15. is that just an estimate? Because from the graph I'm using it's:

f (-0.4) 8.8 (local max)

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