Answer:
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Step-by-step explanation:
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Answer:
(2x-1)(x-7)
Step-by-step explanation:
Answer:
The absolute maximum and minimum is
Step-by-step explanation:
We first check the critical points on the interior of the domain using the
first derivative test.
![f_x=y-4=0](https://tex.z-dn.net/?f=f_x%3Dy-4%3D0)
![f_y=x=0](https://tex.z-dn.net/?f=f_y%3Dx%3D0)
The only solution to this system of equations is the point (0, 4), which lies in the domain.
![f_{xx}=0, \;f_{yy}=0\; \text{and}\; f_{xy}=-1](https://tex.z-dn.net/?f=f_%7Bxx%7D%3D0%2C%20%5C%3Bf_%7Byy%7D%3D0%5C%3B%20%5Ctext%7Band%7D%5C%3B%20f_%7Bxy%7D%3D-1)
![\Rightarrow f_{xx}f_{yy}-f_{xy}=o-1=-1](https://tex.z-dn.net/?f=%5CRightarrow%20f_%7Bxx%7Df_%7Byy%7D-f_%7Bxy%7D%3Do-1%3D-1%3C0)
is a saddle point.
Boundary points - ![(4,0), (-4,0), (0,16)](https://tex.z-dn.net/?f=%284%2C0%29%2C%20%20%28-4%2C0%29%2C%20%280%2C16%29)
Along boundary ![y=16-x^2](https://tex.z-dn.net/?f=y%3D16-x%5E2)
![f=x(16-x^2)-4x](https://tex.z-dn.net/?f=f%3Dx%2816-x%5E2%29-4x)
![=16x-x^3-4x](https://tex.z-dn.net/?f=%3D16x-x%5E3-4x)
![\Rightarrow f^'=16-3x^2-4=0](https://tex.z-dn.net/?f=%5CRightarrow%20f%5E%27%3D16-3x%5E2-4%3D0)
![\Rightarrow 3x^2=12](https://tex.z-dn.net/?f=%5CRightarrow%203x%5E2%3D12)
![\Rightarrow x=\pm2,\;\;y=14](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D%5Cpm2%2C%5C%3B%5C%3By%3D14)
Values of f(x) at these points.
![\begin{array}{}(4,0)=-16\\(-4,0)=16\\(0,16)=0\\(2,14)=20\\(-2,14)=-20\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7B%7D%284%2C0%29%3D-16%5C%5C%28-4%2C0%29%3D16%5C%5C%280%2C16%29%3D0%5C%5C%282%2C14%29%3D20%5C%5C%28-2%2C14%29%3D-20%5Cend%7Barray%7D)
Therefore, the absolute maximum and minimum is
Answer:
1) d < -2
2) b < 3
Step-by-step explanation:
1) d+3< 1
subtract both sides by 3
d+3 -3 < 1-3
d<-2
2) b+6< 9
subtract both sides by 6
b+6 -6 < 9 -6
b< 3