-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.
Profit=p(-p^2+33p+9)-9(-p^2+33p+9)+100
How do I simplify this so I can take the derivative
For Further Reading
* 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?
11 answers
I got 24 and 4.
p - 24 = 0, p + 4 = 0
p = 24, p = -4
Then, plug each of those into your original PROFIT equation to get the max.
p = 24, p = -4
Then, plug each of those into your original PROFIT equation to get the max.
With -4 I got 508 and with 24 I got -6893
What did I do wrong? This makes no sense
What did I do wrong? This makes no sense
Profit=p(-p^2+33p+9)-9(-p^2+33p+9)+100
If you plugged it into that, check your algebra.
If you plugged it into that, check your algebra.
I got 20755 when I plugged 24 in and -685 when I plugged 4 in, is this correct?
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.
Anyway, forget the -4. p=24 will give you the greatest profit. All you have to do is plug and chug.
But how is it -4, I am confused
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
We do that by setting each parenthesis equal to 0.
p + 4 = 0
Subtract 4 from both sides.
p = -4
okay sorry. How can I be certain that the profit is being maximized?
I'm not sure. Try the general justification for a maximum:
The derivative is changing from negative to positive.
The derivative is changing from negative to positive.
11 answers