It is sufficient to give the correct answer. a) Someone asks you to study a function f (r) for small input vectors r. What should be your first reaction? b) Give an example of a parameterized curve r(t) = (x(t), y(t)) such that t r(0) = (0, 1), r(1) = (1, 2), |r' ( 1/2 )|= v2 c) Enter a continuous function f (x, y) that is not derivable at the point (0, 1) and has a local minimum with the value 2 at this point

It is sufficient to give the correct answer. a) Someone asks you to study a function f (r) for small input vectors r. What should be your first reaction? b) Give an example of a parameterized curve r(t) = (x(t), y(t)) such that t r(0) = (0, 1), r(1) = (1, 2), |r' ( 1/2 )|= v2 c) Enter a continuous function f (x, y) that is not derivable at the point (0, 1) and has a local minimum with the value 2 at this point

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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Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

1. It is sufficient to give the correct answer.
a) Someone asks you to study a function f (r) for small input vectors r. What should be your
first reaction?
b) Give an example of a parameterized curve r(t) = (x(t), y(t)) such that t r(0) = (0, 1), r(1) =
(1, 2), [r ( 1/2 )|= v2
c) Enter a continuous function f (x, y) that is not derivable at the point (0, 1) and has a local
minimum with the value 2 at this point
d) Is there any function f (x, y, z) such that all its level quantities are plane x + 3y + z = C and
which are not lines? Enter one in this case
e) Consider the function f(x, y) = y(y-x^2 ). In which areas of the planet are f positive,
negative, resp 0? Draw a figure.

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