As in the previous question, let f, g: [−1, 1] → R be smooth strictly increasing functions, and define a smooth curve y: [−1, 1] → R² by y(t) = (ƒ(t), g(t)). Which of the following statements about the regularity of y are true? Select one or more: a. For any such f and g, y is regular. b. If f and g both have critical points then y is not regular. c. If one of the functions for g has a critical point, then y is not regular. d. If both f and g have no critical points then y is regular. e. If one of the functions for g has no critical points, then y is regular. y is regular if and only if both of the functions f and g have no critical points. Og. y is regular if and only if one of the functions for g has no critical points.

As in the previous question, let f, g: [−1, 1] → R be smooth strictly increasing functions, and define a smooth curve y: [−1, 1] → R² by y(t) = (ƒ(t), g(t)). Which of the following statements about the regularity of y are true? Select one or more: a. For any such f and g, y is regular. b. If f and g both have critical points then y is not regular. c. If one of the functions for g has a critical point, then y is not regular. d. If both f and g have no critical points then y is regular. e. If one of the functions for g has no critical points, then y is regular. y is regular if and only if both of the functions f and g have no critical points. Og. y is regular if and only if one of the functions for g has no critical points.

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.CR: Chapter 9 Review

Problem 6CR

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