Turning Points

mathdad said:
Is this not what I posted?
Click to expand...
Yes, it is not what you posted.

In post #17, Dr. Peterson quoted what you posted. Please look at it. You didn't type \(\sqrt{2}\). You typed symbolic representations, instead.

\(\;\)
 
Otis said:
Yes, it is not what you posted.

In post #17, Dr. Peterson quoted what you posted. Please look at it. You didn't type \(\sqrt{2}\). You typed symbolic representations, instead.

\(\;\)
Click to expand...

Otis:

It is a typo at my end. I use my cell for everything. I do not have a PC or laptop in my room.

The cell phone keyboard is VERY TINY compared to my FAT fingers. I understand the question and will post the entire solution from A to E, if not on Monday, Tuesday for sure. Please, give me some credit. I am not retarded.
 
MarkFL said:
Yes, and I have certainly made my fair share of those over the years. Most of us have. The point of bringing it up though is not to shame you, but to make it clear to anyone reading the thread that it is not what was intended, for clarity.
Click to expand...

Thank you.
 
No, it was not! What you posted, in response #14, was
"Zeros: x = 0, -sqrt{x}, sqrt{x}

Multiplicity for 0 is 2.
Multiplicity for -sqrt{x} and sqrt{x} is 1."

You had sqrt{x} where you should have had sqrt{2}.
 
mathdad said:
... I am not retarded.
Click to expand...
Of course you're not retarded. But you often act thin-skinned. You take constructive criticism and correction as personal attacks. People point out mistakes to help you learn because learning math is a process of making mistakes, understanding what went wrong, fixing them and moving forward.

Also, when somebody quotes your typing and says you may have made a typo, then you ought to examine your typing, to try figure out what they're talking about. I've seen many instances where you didn't seem to pay attention to replies you've received. Instead of reading carefully or checking your work, you seem to jump to false conclusions, think you're under attack or simply decide you no longer have interest in the thread.

I make mistakes regularly (sometimes, every day of the week). When I make a mistake on the boards, I hope somebody sees it and lets me know right away (so I can fix it). I'm not offended by that; I'm thankful.

?
 
MarkFL said:
I would begin by writing the function as:

[MATH]f(x)=-2x^2(x+\sqrt{2})(x-\sqrt{2})[/MATH]
Now it's real easy to see each zero and its multiplicity. Can you state them?
Click to expand...

Part A

The zeros and the multiplicity for each respectively are: 0, -sqrt{2}, sqrt{2}; multiplicity 1 for all three zeros.

Part B

Based on the result in part A, the multiplicity is 1 and thus the graph crosses the x-axis.

Part C

Near 0:

I know that -2x^2 leads to x = 0. Plug x = 0 into the other two factors.

(x + sqrt{2})(x + sqrt{2})

(0 + sqrt{2})(0 - sqrt{2})

(sqrt{2})(-sqrt{2}) = -sqrt{4} = -2.

y = -2(-2x^2)

y = 4x^2

Near -sqrt{2}:

I know that solving x + sqrt{2} for x leads to -sqrt{2}. Plug into the other two factors.

-2(-sqrt{2})^2(-sqrt{2} - sqrt{2}

-2(2)(-2sqrt{2})

(-4)(-2sqrt{2})

8sqrt{2}

y = 8sqrt{2}(x + sqrt{2})

Near sqrt{2}:

I know that solving x - sqrt{2} for x leads to sqrt{2}. Plug into the other two factors.

After doing the math, I got
y = -8sqrt(x - sqrt{2}).

Part D

Using Wolfram, I see 3 turning points.

See here:

m.wolframalpha.com

Wolfram|Alpha: Making the world’s knowledge computable

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.
m.wolframalpha.com m.wolframalpha.com

Part D

I need to find the power function that the graph of f resembles for large values of | x |. Back to the original function given.


f(x) = (-2x^2)(x^2 - 2)

f(x) = -2x^4 + 4x^2

The needed power function is
f(x) = -2x^4.

What do you say?
 
You must log in or register to reply here.
Top