figure below shows the level curves of a function f(x, y) around a maximum or minimum, M. The z- and y-axes are along the bottom and left edge of the figure, respectively. of the points P and Q has coordinates (₁, 1) and the other has coordinates (22, 32). Suppose b>0 and c < 0. Consider the two linear approximations to f given by f(z,y)≈a+b(z-7₁)+cy-y₁), f(z,y)≈k+m(z-7₂) + n(y-2).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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E Q11

The figure below shows the level curves of a function f(x, y) around a maximum or minimum, M. The z- and y-axes are along the bottom and left edge of the figure, respectively.
One of the points P and Q has coordinates (₁, 1) and the other has coordinates (22, 32). Suppose b>0 and c < 0. Consider the two linear approximations to f given by
f(x,y) ≈a+b(x-₁)+c(y - y₁),
and
(a) What is the relationship between the values of a and k?
(Give your answer as an equation.)
(b) What are the coordinates of P?
V
aximum or a minimum??
n you say about the sign of the constants m and n?
(x1,y1)
(x2,y2)
mu, and
n? ✓0.
Submit answer
f(x,y) ≈k+m(x − T2) + n(y — Y2).
Transcribed Image Text:The figure below shows the level curves of a function f(x, y) around a maximum or minimum, M. The z- and y-axes are along the bottom and left edge of the figure, respectively. One of the points P and Q has coordinates (₁, 1) and the other has coordinates (22, 32). Suppose b>0 and c < 0. Consider the two linear approximations to f given by f(x,y) ≈a+b(x-₁)+c(y - y₁), and (a) What is the relationship between the values of a and k? (Give your answer as an equation.) (b) What are the coordinates of P? V aximum or a minimum?? n you say about the sign of the constants m and n? (x1,y1) (x2,y2) mu, and n? ✓0. Submit answer f(x,y) ≈k+m(x − T2) + n(y — Y2).
The figure below shows the level curves of a function f(z,y) around a maximum or minimum, M. The z- and y-axes are along the bottom and left edge of the figure, respectively.
One of the points P and Q has coordinates (₁, 1) and the other has coordinates (#2, 32). Suppose b>0 and c < 0. Consider the two linear approximations to f given by
f(x,y) ≈a+b(x − x₁) + c(y — Y₁),
and
(a) What is the relationship between the values of a and k?
(Give your answer as an equation.)
(b) What are the coordinates of P?
?
(c) Is M a maximum or a minimum??
(d) What can you say about the sign of the constants m and n?
m ?0, and
0.
n
>=
iswer
Answers (in progress)
f(z,y) ≈k+m(1 – 1₂) + n(y-Y2).
Transcribed Image Text:The figure below shows the level curves of a function f(z,y) around a maximum or minimum, M. The z- and y-axes are along the bottom and left edge of the figure, respectively. One of the points P and Q has coordinates (₁, 1) and the other has coordinates (#2, 32). Suppose b>0 and c < 0. Consider the two linear approximations to f given by f(x,y) ≈a+b(x − x₁) + c(y — Y₁), and (a) What is the relationship between the values of a and k? (Give your answer as an equation.) (b) What are the coordinates of P? ? (c) Is M a maximum or a minimum?? (d) What can you say about the sign of the constants m and n? m ?0, and 0. n >= iswer Answers (in progress) f(z,y) ≈k+m(1 – 1₂) + n(y-Y2).
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