(b) Compute the partial derivative fy at the point (x, y) = (1, 1), or show that it does not exist. (o) Comput the lingorizotion of fl ) ot the noint (r a4) (1 1)

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Chapter2: Second-order Linear Odes
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Need help with part b). Please explain each step. Thank you :)

3. Let f : R2 → R be the function f(x,y) = |x – 1| · |y – 1|3.
(a) Compute the partial derivative fr at the point (r, y) = (1, 1), or show that it does not
exist.
(b) Compute the partial derivative fy at the point (r, y) = (1, 1), or show that it does not
exist.
(c) Compute the linearization of f(x,y) at the point (x, y) = (1,1).
(d) Determine whether f(x, y) is differentiable at the point (r, y) = (1, 1).
(e) Does the linearization approximate f(r, y) near the point (1, 1)? Justify your answer.
Transcribed Image Text:3. Let f : R2 → R be the function f(x,y) = |x – 1| · |y – 1|3. (a) Compute the partial derivative fr at the point (r, y) = (1, 1), or show that it does not exist. (b) Compute the partial derivative fy at the point (r, y) = (1, 1), or show that it does not exist. (c) Compute the linearization of f(x,y) at the point (x, y) = (1,1). (d) Determine whether f(x, y) is differentiable at the point (r, y) = (1, 1). (e) Does the linearization approximate f(r, y) near the point (1, 1)? Justify your answer.
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