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Dvinal [7]
3 years ago
15

Which of the following situations can be described by the equation 2x – 4 = 10?

Mathematics
1 answer:
chubhunter [2.5K]3 years ago
8 0

Step-by-step explanation:

Add 44 to both sides.

2x=10+4

2x=10+4

2 Simplify 10+410+4 to 1414.

2x=14

2x=14

3 Divide both sides by 22.

x=\frac{14}{2}

x=

2

14

4 Simplify \frac{14}{2}

2

14

to 77.

x=7

x=7

Done

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We have critical points whenever both partial derivatives vanish:

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4y^3-4x=0\implies y^3=x=y^{1/3}\implies y^6=y\implies y=0,y=-1,y=1
\begin{cases}y=0\implies x=0\\y=-1\implies x=-1\\y=1\implies x=1\end{cases}

The Hessian is

\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}12x^2&-4\\-4&12y^2\end{bmatrix}
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At (-1, -1), we have \det\mathbf H(-1,-1)=128>0 and f_{xx}(-1,-1)=12>0, so (-1, -1) is a local minimum.

At (1, 1), we have \det\mathbf H(1,1)=128>0 and f_{xx}(1,1)=12>0, so (1, 1) is also a local minimum.

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