Homework Help: Calc

Posted by Ben on Sunday, November 25, 2007 at 8:20pm.

Profit=p(-p^2+33p+9)-9(-p^2+33p+9)+100

How do I simplify this so I can take the derivative

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* Calc - Michael, Sunday, November 25, 2007 at 4:17pm

Profit=p(-p^2+33p+9)-9(-p^2+33p+9)+100

p(-p^2 + 33p + 9)
Just distribute the p in.

-9(-p^2 + 33p + 9)
Find the derivative of the (-p^2 + 33p + 9) and then multiply it by -9. You can distribute the -9 in at the beginning, but it's not necessary.

+100
The derivative of a consonant is 0.

I hope that helps. If you have any questions, let me know.

o Calc - Ben, Sunday, November 25, 2007 at 6:55pm

I got -3p^2+84p+298

Is this right?

+ Calc - Ben, Sunday, November 25, 2007 at 6:58pm

I made a mistake it should be -296 but I do not think this is right because I know I am supposed to factor this and I cannot get it to factor.

o Calc - Ben, Sunday, November 25, 2007 at 7:08pm

That is wrong too Now I got
-3p^2+84p-288

Is this right, I cannot figure out how to factor it though

+ Calc - Michael, Sunday, November 25, 2007 at 7:31pm

Yes, that's correct. To factor, you can take out a common number. (Take out a negative to make it easier to work with, too.) Try that, and see what you get.

* Calc - Ben, Sunday, November 25, 2007 at 7:36pm

I got -3(p^2-28p+96)

Now How do I factor this further I need to eventually set it equal to zero

o Calc - Michael, Sunday, November 25, 2007 at 7:42pm

Don't worry about setting it equal to 0. Since we're factoring, it is equal to 0. (You can write that = 0 in your work if you want.)

That's difficult to continue factoring. Here's a hint: 4 x 24 is 96.

+ Calc - Ben, Sunday, November 25, 2007 at 7:58pm

Wait, the other one is wrong, it is
-3(p-24)(p-4).
So the max possible weekly profit is $24 dollars???

Now how do I determine the max possible weekly profit and be certain the profit is maximized?

* Calc - Ben, Sunday, November 25, 2007 at 7:54pm

So is it -3(p-24)(p+4)
I have to find which will give me my largest profit so I need to set them equal to zero. That would then be $24, right?
How do I determine max possible weekly profit?

o Calc - Michael, Sunday, November 25, 2007 at 8:02pm

Don't forget that factoring gives you the x-intercepts of an equation. Maxima are the highest and lowest y-values.

Have you learned the First Derivative Test?

+ Calc - Ben, Sunday, November 25, 2007 at 8:06pm

No, But should I charge $24 to get the largest weekly profit?

Calc - Michael, Sunday, November 25, 2007 at 8:31pm
-3(p-24)(p+4) = 0

Solve that for p. You should get two answers.

Then, plug each of those into your original PROFIT equation to get the max.
- Calc - Ben, Sunday, November 25, 2007 at 8:35pm
  I got 24 and 4.
  - Calc - Michael, Sunday, November 25, 2007 at 8:38pm
    p - 24 = 0, p + 4 = 0
    p = 24, p = -4
    
    Then, plug each of those into your original PROFIT equation to get the max.
- Calc - Ben, Sunday, November 25, 2007 at 8:44pm
  With -4 I got 508 and with 24 I got -6893
  What did I do wrong? This makes no sense
  - Calc - Michael, Sunday, November 25, 2007 at 8:50pm
    Profit=p(-p^2+33p+9)-9(-p^2+33p+9)+100
    
    If you plugged it into that, check your algebra.
    - Calc - Ben, Sunday, November 25, 2007 at 8:54pm
      I got 20755 when I plugged 24 in and -685 when I plugged 4 in, is this correct?
      - Calc - Michael, Sunday, November 25, 2007 at 8:58pm
        No, that's still not right. You should have plugged in 24 and NEGATIVE 4.
        
        Anyway, forget the -4. p=24 will give you the greatest profit. All you have to do is plug and chug.
        
        Calc - Ben, Sunday, November 25, 2007 at 8:59pm
        But how is it -4, I am confused
        
        Calc - Michael, Sunday, November 25, 2007 at 9:00pm
        We were solving -3(p-24)(p+4) = 0.
        
        We do that by setting each parenthesis equal to 0.
        
        p + 4 = 0
        Subtract 4 from both sides.
        
        p = -4
        
        Calc - Ben, Sunday, November 25, 2007 at 9:02pm
        okay sorry. How can I be certain that the profit is being maximized?
        
        Calc - Michael, Sunday, November 25, 2007 at 9:11pm
        I'm not sure. Try the general justification for a maximum:
        
        The derivative is changing from negative to positive.

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