Please help with calculus hw (check my answers)

[marksason]

Hello

http://img123.imageshack.us/img123/9923 ... 7pmpi8.jpg

since everyone had problems understanding what I was talking about I scanned it. I need help with problems 7, 8, and 12. But please check the others too make sure there correct too. As you can all see I have tried I just havent mastered the rules yet. Just let me know if I am on the correct path.

 

[stapel]

1) Find the first and second derivatives of -2 / x^2 +2x +1

As written, the expression is (-2/x²) + 2x + 1. Is this what you meant? Or did you mean something more like (-2)/(x² + 2x + 1)?

To differentiate, try using the Quotient Rule.

I get up to 6(4x^2 +3x +1) = 0 I just cant figure out how to solve for x.

How do you get to this point? (Showing your steps would be helpful.) Did you not take algebra before calculus, and that's why you're not familiar with the Quadratic Formula?

Also these I got these answers...

Answers to what? Exercises have to be more than just expressions; there must be instructions. Lacking such, there is no way to evaluate your "work". Sorry.

Eliz.

 

[marksason]

1) Find the first and second derivatives of -2 / x^2 +2x +1

As written, the expression is (-2/x²) + 2x + 1. Is this what you meant? Or did you mean something more like (-2)/(x² + 2x + 1)?

To differentiate, try using the Quotient Rule.

I get up to 6(4x^2 +3x +1) = 0 I just cant figure out how to solve for x.

How do you get to this point? (Showing your steps would be helpful.) Did you not take algebra before calculus, and that's why you're not familiar with the Quadratic Formula?

Also these I got these answers...

Answers to what? Exercises have to be more than just expressions; there must be instructions. Lacking such, there is no way to evaluate your "work". Sorry.

Eliz.

(-2)/(x^2 + 2x + 1)


thats what I ment for the first one for the last part my instructions are just to differentiate. That is all (its most likely using chain rule and those related rules..). I am not too familair with the quadratic formula as I took algebra a long time ago. And i find it too difficult. If you can just show the steps and explain I might be able to learn it better. (I have looked online for help and I just cant figure out) Sorry please help.

 

[soroban]

Hello, marksason!

Here are the first two.
I can't read the last one . . .

1) Find the first and second derivatives of: \(\displaystyle y \:=\:\frac{-2}{x^2\,+\,2x\,+\,1}\)

We have: \(\displaystyle \:y \:=\:\frac{-2}{(x\,+\,1)^2} \:=\:-2(x\,+\,1)^{-2}\)

Then: \(\displaystyle \:y'\;=\;4(x\,+\,1)^{-3}\)

And: \(\displaystyle \:y'' \;=\;-12(x\,+\,1)^{-4}\)

2) Find absolute max and minimum values of the function, if they exist.
. . \(\displaystyle f(x) \:= \:-8x^3\,+\,9x^2\,+\,6x\,-\,2\)

We have: \(\displaystyle \:f'(x)\:=\:-24x^2\,+\,18x\,+\,6\;=\;0\)

Divide by -6: \(\displaystyle \:x^2\,-\,3x\,-\,1\:=\:0\)

. . which factors: \(\displaystyle \x\,-\,1)(4x\,+\,1)\:=\:0\)

. . and has roots: \(\displaystyle \:x\:=\:1,\,-\frac{1}{4}\)


The second derivative is: \(\displaystyle \:f''(x) \:=\:-48x\,+\,18\)

\(\displaystyle f''(1)\:=\:-48(1)\,+\,18\:=\:-30\) . . . negative, concave down: \(\displaystyle \cap\)

. . Therefore, a relative maximum at \(\displaystyle (1,5)\)

\(\displaystyle f''\left(-\frac{1}{4}\right)\:=\:-48\left(-\frac{1}{4}\right)\,+\,18\:=\:+30\) . . . positive, concave up: \(\displaystyle \cup\)

. . Therefore, a relative minimum at \(\displaystyle \left(-\frac{1}{4},\,-\frac{45}{16}\right)\)

 

[marksason]

hey thanks for the help here is the 2nd half that your all having problem understanding the way I wrote it. Here it is. Please can you just check my answers for all of them but my main concerns are 7,8 and 12. But if you can just check them all for me.

Here are the problems just view the image of the paper.
http://img123.imageshack.us/img123/9923 ... 7pmpi8.jpg

 

[marksason]

Just so you all know I updated my orginal post with image files please since you all did not understand what I was trying to say just read my original post and help me in these questions just check to see if there right.