Consider the function f : R² fy(x, y) = (a) Compute the partial derivatives at the point (1, 0): fx(x, y) = 3 X fxx (x, y) = fxy(x, y) = fyx (x, y) = fyy(x, y) = 2 ✓ 1 X 1 X 1 X R given by 1 X f(x, y) = x²y + sin(xy) + 1 (b) (1, 0) is a local maximum ♦ 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 0 ✔x+ 1 xy+ z = 0 X (d) If x = (s² +1²) and y = si - 1², then at the point (s, t) = (1, 1), af dt (e) The maximum rate of change of f(x, y) at the point (x, y) = (1, 0) is 1 X is equal to 0 x

Consider the function f : R² fy(x, y) = (a) Compute the partial derivatives at the point (1, 0): fx(x, y) = 3 X fxx (x, y) = fxy(x, y) = fyx (x, y) = fyy(x, y) = 2 ✓ 1 X 1 X 1 X R given by 1 X f(x, y) = x²y + sin(xy) + 1 (b) (1, 0) is a local maximum ♦ 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 0 ✔x+ 1 xy+ z = 0 X (d) If x = (s² +1²) and y = si - 1², then at the point (s, t) = (1, 1), af dt (e) The maximum rate of change of f(x, y) at the point (x, y) = (1, 0) is 1 X is equal to 0 x

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.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...

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