. Let f: R²R where f(x, y) = √√√1-x² - y² and c = (0, -2). (a) Find and simplify Df(c). (b) Find and simplify f(c) + L((x, y) — c). (c) What is the equation of the tangent plane to the graph of z = √1-2² - y² through the point (0, -, f(c))?
. Let f: R²R where f(x, y) = √√√1-x² - y² and c = (0, -2). (a) Find and simplify Df(c). (b) Find and simplify f(c) + L((x, y) — c). (c) What is the equation of the tangent plane to the graph of z = √1-2² - y² through the point (0, -, f(c))?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.4: Definition Of The Derivative
Problem 6YT
Related questions
Question
![2. Let ƒ: R² → R where f(x, y) = √1 - x² - y² and c = (0,-2).
(a) Find and simplify Df(c).
(b) Find and simplify f(c)+L((x, y) — c).
-
(c) What is the equation of the tangent plane to the graph of z =
√1 - x² - y² through the point (0, -2, f(c))?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79599c56-a340-49a0-b0ff-829b3947a798%2F81c590e4-acb7-4ebc-b181-05821faf485f%2Flurx5ps_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let ƒ: R² → R where f(x, y) = √1 - x² - y² and c = (0,-2).
(a) Find and simplify Df(c).
(b) Find and simplify f(c)+L((x, y) — c).
-
(c) What is the equation of the tangent plane to the graph of z =
√1 - x² - y² through the point (0, -2, f(c))?
![10:41
←
Expert Answer Ⓒ
Step1
a)
⇒
Step2
b)
(a)
af
dx
(c)
af
ay
=)
=
(b) f(c) + L ((x, y) = c)
and
Hence,
f (x, y) =
=
=>
z =
D f(c) = (cat))
ale)
2x
g=
2 y
əg
ax
=)
93
az
8+ (4,4) (x-2, 4-2)
8 + 4(x-2) + 4 (5-2).
2
x² + y²
-1
equation of
=
a
)
x² + y2
x² + y²_z = 0
a = 4
af
ax
at 10 =
4x + 4y-2 = 8
?
= (4,4)
(2² +2²)+L((x,y)-(2,23)
8 + L ((x-2, y-2))
23
25 = 23
ay
C = (2,2)
= 4
f(c) = 8
tangent plane
4 (x-2) + + (y-2) -1 (2-8) = 0
ag
=>
- 3x1.-
ax
IS
29
dy
√x
= 4
Equation of this plane
(x-) +33 (5-2)
-1 (2-0) = 0
8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79599c56-a340-49a0-b0ff-829b3947a798%2F81c590e4-acb7-4ebc-b181-05821faf485f%2F5j3td86_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10:41
←
Expert Answer Ⓒ
Step1
a)
⇒
Step2
b)
(a)
af
dx
(c)
af
ay
=)
=
(b) f(c) + L ((x, y) = c)
and
Hence,
f (x, y) =
=
=>
z =
D f(c) = (cat))
ale)
2x
g=
2 y
əg
ax
=)
93
az
8+ (4,4) (x-2, 4-2)
8 + 4(x-2) + 4 (5-2).
2
x² + y²
-1
equation of
=
a
)
x² + y2
x² + y²_z = 0
a = 4
af
ax
at 10 =
4x + 4y-2 = 8
?
= (4,4)
(2² +2²)+L((x,y)-(2,23)
8 + L ((x-2, y-2))
23
25 = 23
ay
C = (2,2)
= 4
f(c) = 8
tangent plane
4 (x-2) + + (y-2) -1 (2-8) = 0
ag
=>
- 3x1.-
ax
IS
29
dy
√x
= 4
Equation of this plane
(x-) +33 (5-2)
-1 (2-0) = 0
8
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