3. Let f R2 R be a function. (i) Explain in your own words the relationship between the existence of all partial derivatives of f and differentiability of f at a point x = R². (ii) Consider R2 → R defined by : [5 Marks] f(x1, x2) = |2x1x2|1/2 Show that af af -(0,0) = 0 and -(0, 0) = 0, Jx1 მx2 but f is not differentiable at (0,0). [10 Marks]
3. Let f R2 R be a function. (i) Explain in your own words the relationship between the existence of all partial derivatives of f and differentiability of f at a point x = R². (ii) Consider R2 → R defined by : [5 Marks] f(x1, x2) = |2x1x2|1/2 Show that af af -(0,0) = 0 and -(0, 0) = 0, Jx1 მx2 but f is not differentiable at (0,0). [10 Marks]
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 50E
Related questions
Question
![3.
Let f R2 R be a function.
(i) Explain in your own words the relationship between the
existence of all partial derivatives of f and differentiability of f at a
point x = R².
(ii)
Consider R2 → R defined by
:
[5 Marks]
f(x1, x2) = |2x1x2|1/2
Show that
af
af
-(0,0) = 0 and
-(0, 0) = 0,
Jx1
მx2
but f is not differentiable at (0,0).
[10 Marks]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd66c7573-6777-48ff-9bfb-9b3df1a769a6%2Ff9987b0c-66e7-49ef-9cfb-6637c4b76ab4%2Fz7vzp7q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.
Let f R2 R be a function.
(i) Explain in your own words the relationship between the
existence of all partial derivatives of f and differentiability of f at a
point x = R².
(ii)
Consider R2 → R defined by
:
[5 Marks]
f(x1, x2) = |2x1x2|1/2
Show that
af
af
-(0,0) = 0 and
-(0, 0) = 0,
Jx1
მx2
but f is not differentiable at (0,0).
[10 Marks]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage