# Determine whether the given function is linear or nonlinear. If the function is nonlinear, explain why. [Hint:Recall that a linear function is of the form f (x1; : : : ; xn) = c1x1 + + cnxn where c1; : : : ; cn are constants.](a) f (x; y) = x + 2y(b) g(x1; x2; x3) = cos(x1 + x2 + x3)(c) h(x1; x2; x3; x4) = 6x1 45 x2 + 178 x3 x4(d) k(x1; : : : ; xn) = 3(x1 + + xn 1)(e) f (x1; x2) = x21 x1x2

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.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...
Question

Determine whether the given function is linear or nonlinear. If the function is nonlinear, explain why. [Hint:

Recall that a linear function is of the form f (x1; : : : ; xn) = c1x1 + + cnxn where c1; : : : ; cn are constants.]

(a) f (x; y) = x + 2y

(b) g(x1; x2; x3) = cos(x1 + x2 + x3)

(c) h(x1; x2; x3; x4) = 6x1 45 x2 + 178 x3 x4

(d) k(x1; : : : ; xn) = 3(x1 + + xn 1)

(e) f (x1; x2) = x21 x1x2

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