Let f(x, y) 2x²y² 4 x +y = (x, y) = (0,0) , (x, y) = (0,0) Show that the first order partial derivatives exist at (0, 0) but the function is not differentiable at (0, 0).

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.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 20E
icon
Related questions
Question
Let f(x, y)
2x²y²
4
x +y
=
(x, y) = (0,0)
, (x, y) = (0,0)
Show that the first order partial derivatives exist at (0, 0) but the function is not
differentiable at (0, 0).
Transcribed Image Text:Let f(x, y) 2x²y² 4 x +y = (x, y) = (0,0) , (x, y) = (0,0) Show that the first order partial derivatives exist at (0, 0) but the function is not differentiable at (0, 0).
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,