Question
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?
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?
Answers
Michael
-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.
Solve that for p. You should get two answers.
Then, plug each of those into your original PROFIT equation to get the max.
Ben
I got 24 and 4.
Michael
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.
Ben
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
Michael
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.
Ben
I got 20755 when I plugged 24 in and -685 when I plugged 4 in, is this correct?
Michael
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.
Ben
But how is it -4, I am confused
Michael
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
Ben
okay sorry. How can I be certain that the profit is being maximized?
Michael
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.