e) The maximum rate of change of f(x, y) at the point (x, y) = (1, 0) is
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need help with part e). Thank you :)
Transcribed Image Text:Consider the function f : R2
→ R given by
f(x, y) = x²y + sin(xy) + 1
(a) Compute the partial derivatives at the point (1,0):
fx(x, y) =
fy(x, y) =
fxx(x, y) =
fxy(x, y) =
fyx (x, y) =
f yy(x, y) =
(b) (1, 0) is
of the function f.
(c) The tangent plane to the graph of z = f(x, y) at the point (1, 0, 1) can be described by the equation
x+
y+ z =
se
dt
(d) If x = (s² + t²) and y = s – t², then at the point (s, t) = (1, 1),
is equal to
(e) The maximum rate of change of f(x, y) at the point (x, y) = (1, 0) is
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