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2 years ago

❗️5 points❗️ 5. state the slope of the line. A. -2 B. 0 C. 1 D. Undefined

Mathematics

2 answers:

wlad13 [49]2 years ago

5 0

Answer:

B. 0

Step-by-step explanation:

Use the following formula to solve for slope:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (0 , -2)

(x₂ , y₂) = (2 , -2)

Plug in the corresponding numbers to the corresponding variables:

m = (-2 - (-2))/(2 - 0)

Simplify:

m = (-2 + 2)/(2 - 0)

m = 0/2 = 0

B. 0 is your slope.

Anna35 [415]2 years ago

4 0

Hey there! :)

Answer:

B. 0

Step-by-step explanation:

On the graph, the line is a horizontal line. This means that there is no change in the y-value across the domain.

Thus, the graph has a slope of 0.

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The Hessian matrix for this function looks like

$H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}-18e^y&-18xe^y\\-18xe^y&9e^y(2-x^2+4y+y^2)\end{bmatrix}$

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At $(0,0)$ , you have a saddle point since the determinant reduces to -324, so $(0,0,0)$ is the saddle point.

At $(0,-2)$ , the determinant is $\dfrac{324}{e^4}>0$ and $f_{xx}(0,-2)=-\dfrac{18}{e^2}$ , so $\left(0,-2,\dfrac{36}{e^2}\right)$ is a local maximum.

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Answer:
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