Step-by-step explanation:
First you need to get x on one side by subtracting it from either side
Second step the side you subtracted the x to you need to get rid of the number like the number 5
Third step you need to separate the number and x since they are being multiplied to be put together you need to do the opposite and divide on both sides
38/9
46/7
44/5
11/4
19/2
11/6
23/3
41/8
52/7
34/5
Answer:
The Maximum value is ![P(x)=2076.227](https://tex.z-dn.net/?f=P%28x%29%3D2076.227)
Step-by-step explanation:
Given,
(equation-1)
Differentiate above equation with respect to 'x',
--- (equation 2)
Again differentiate above equation with respect to 'x',
------- (equation 3)
From equation-2 we see,
The value of
,
,
.
Now, for maximum or minimum, the first derivative must be 0.
For maximum, ![P''(x)](https://tex.z-dn.net/?f=P%27%27%28x%29%3C0)
So, ![P'(x)=-0.0039\times x^{2} +0.6x+8 = 0](https://tex.z-dn.net/?f=P%27%28x%29%3D-0.0039%5Ctimes%20x%5E%7B2%7D%20%2B0.6x%2B8%20%3D%200)
Using the quadratic formula, we find the roots of
![x=\frac{-0.6\pm \sqrt{0.6^{2}-4\times -0.0039\times 8 } }{2\times -0.0039}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-0.6%5Cpm%20%5Csqrt%7B0.6%5E%7B2%7D-4%5Ctimes%20-0.0039%5Ctimes%208%20%7D%20%7D%7B2%5Ctimes%20-0.0039%7D)
![x=\frac{-0.6\pm 0.696}{-0.0078}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-0.6%5Cpm%200.696%7D%7B-0.0078%7D)
or ![x=166.15](https://tex.z-dn.net/?f=x%3D166.15)
For
,
![P''(x)=(6\times-0.0013\times -12.3 )+(2\times 0.3)](https://tex.z-dn.net/?f=P%27%27%28x%29%3D%286%5Ctimes-0.0013%5Ctimes%20-12.3%20%29%2B%282%5Ctimes%200.3%29)
![P''(x)=0.696>0](https://tex.z-dn.net/?f=P%27%27%28x%29%3D0.696%3E0)
Which is minimum value at ![x=-12.3](https://tex.z-dn.net/?f=x%3D-12.3)
And for
,
![P''(x)=(6\times-0.0013\times 166.15 )+(2\times 0.3)](https://tex.z-dn.net/?f=P%27%27%28x%29%3D%286%5Ctimes-0.0013%5Ctimes%20166.15%20%29%2B%282%5Ctimes%200.3%29)
![P''(x)=-0.696< 0](https://tex.z-dn.net/?f=P%27%27%28x%29%3D-0.696%3C%200)
Which is maximum value at ![x=166.15](https://tex.z-dn.net/?f=x%3D166.15)
Plug
in equation-1,
![P(x)=-0.0013\times 166.15^{3} +0.3\times 166.15^{2} +8\times 166.15-372](https://tex.z-dn.net/?f=P%28x%29%3D-0.0013%5Ctimes%20166.15%5E%7B3%7D%20%2B0.3%5Ctimes%20166.15%5E%7B2%7D%20%2B8%5Ctimes%20166.15-372)
![P(x)=2076.227](https://tex.z-dn.net/?f=P%28x%29%3D2076.227)
So the Maximum value is ![P(x)=2076.227](https://tex.z-dn.net/?f=P%28x%29%3D2076.227)