Assignment 29

course Mth 272

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16:47:38
Query problem 7.4.50 (was 7.4.46) slope in x direction and y direction for z=x^2-y^2 at (-2,1,3)

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RESPONSE -->

confidence assessment:

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16:47:56
What is the slope in the x direction at the given point? Describe specifically how you obtained your result.

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RESPONSE -->
derivative with respect of x is 2x, 2(-2) = -4
confidence assessment: 2

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16:48:08
What is the slope in the y direction at the given point? Describe specifically how you obtained your result.

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RESPONSE -->
derivative with respect of y is -2y, -2(1) = -2
confidence assessment: 2

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Good.

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16:48:11

Query problem 7.4.65 (was 7.4.61) all second partials of ln(x-y) at (2,1)

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RESPONSE -->

confidence assessment:

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16:48:23

What is fxx at the given point?

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RESPONSE -->

-1/(x-y)^2

(2,1) = -1/(2-1)^2 = -1

confidence assessment: 2

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16:48:32

What is fyx at the given point?

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RESPONSE -->

1/(x-y)^2

(2,1) = 1/(2-1)^2 = 1

confidence assessment: 2

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16:48:43

What is fxy at the given point?

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RESPONSE -->

1/(x-y)^2

(2,1) = 1/(2-1)^2 = 1

confidence assessment: 2

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16:48:53

What is fyy at the given point?

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RESPONSE -->

-1/(x-y)^2

(2,1) = -1/(2-1)^2 = -1

confidence assessment: 2

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16:49:04

What is fx at the given point?

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RESPONSE -->

1/x-y

confidence assessment: 2

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16:49:13

What is fy at the given point?

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RESPONSE -->

-1/x-y

confidence assessment: 2

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Good.

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16:49:17

Query problem 7.4.68 R = 200 x1 + 200 x2 - 4x1^2 - 8 x1 x2 - 4 x2^2; R is revenue, x1 and x2 production of plant 1 and plant 2

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RESPONSE -->

confidence assessment:

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16:49:29

What is the marginal revenue for plant 1?

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RESPONSE -->

200 - 8(4) - 8(12) = 72

confidence assessment: 2

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16:49:33

What is the marginal revenue for plant 2?

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RESPONSE -->

200 - 8(4) - 8(12) = 72

confidence assessment: 2

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16:49:36

Why should the marginal revenue for plant 1 be the partial derivative of R with respect to x1?

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RESPONSE -->

confidence assessment:

Marginal revenue is the rate at which revenue changes per unit of increased production. The increased production at plant 1 is the change in x1, so we use the derivative with respect to x1.

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16:49:39

Why, in real-world terms, might the marginal revenue for each plant depend upon the production of the other plant?

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RESPONSE -->

confidence assessment:

&& The marginal revenues for each plant may depend on each other if one plant awaits shipment of a part from the other, or if one plant is somewhat slow resulting in a bottleneck. &&

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16:49:42

What is is about the function that ensures that the marginal revenue for each plant will depend on the production of both plants?

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RESPONSE -->

confidence assessment:

The specific reason is that both derivatives contain x1 and x2 terms, so both marginal revenues depend on both the production of plant 1 and of plant 2.

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Assignment 29

Good.

Good.

Marginal revenue is the rate at which revenue changes per unit of increased production. The increased production at plant 1 is the change in x1, so we use the derivative with respect to x1.

&& The marginal revenues for each plant may depend on each other if one plant awaits shipment of a part from the other, or if one plant is somewhat slow resulting in a bottleneck. &&

The specific reason is that both derivatives contain x1 and x2 terms, so both marginal revenues depend on both the production of plant 1 and of plant 2.

&#

This looks good. See my notes. Let me know if you have any questions. &#

Assignment 29

Good.

Good.

** Marginal revenue is the rate at which revenue changes per unit of increased production. The increased production at plant 1 is the change in x1, so we use the derivative with respect to x1. **

*&*& The marginal revenues for each plant may depend on each other if one plant awaits shipment of a part from the other, or if one plant is somewhat slow resulting in a bottleneck. *&*&

** The specific reason is that both derivatives contain x1 and x2 terms, so both marginal revenues depend on both the production of plant 1 and of plant 2. **

&#

This looks good. See my notes. Let me know if you have any questions. &#

Marginal revenue is the rate at which revenue changes per unit of increased production. The increased production at plant 1 is the change in x1, so we use the derivative with respect to x1.

&& The marginal revenues for each plant may depend on each other if one plant awaits shipment of a part from the other, or if one plant is somewhat slow resulting in a bottleneck. &&

The specific reason is that both derivatives contain x1 and x2 terms, so both marginal revenues depend on both the production of plant 1 and of plant 2.