Consider a differentiable function f(x, y) and a curve r(t) = (x(t), y(t)) which is a level curve for f(x, y); that is, f(x(t), y(t)) = constant for all t. Consider a particular fixed t (that is, a particular point on the curve), the gradient of f(x, y) at this point (that is, the vector Vf = Vf(x(t,y(t))and the derivative vector r' = (x'(t), y'(t)). Which from the statements below is true? A The angle between vectors Vf and r' may be equal to any angle between 0 and T. Vectors Vf and r' are orthogonal. (Vectors Vf and r' have the same direction.

Consider a differentiable function f(x, y) and a curve r(t) = (x(t), y(t)) which is a level curve for f(x, y); that is, f(x(t), y(t)) = constant for all t. Consider a particular fixed t (that is, a particular point on the curve), the gradient of f(x, y) at this point (that is, the vector Vf = Vf(x(t,y(t))and the derivative vector r' = (x'(t), y'(t)). Which from the statements below is true? A The angle between vectors Vf and r' may be equal to any angle between 0 and T. Vectors Vf and r' are orthogonal. (Vectors Vf and r' have the same direction.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Consider a differentiable function f(x, y) and a curve r(t) = (x(t), y(t)) which
is a level curve for f(x, y); that is,
f(x(t), y(t)) = constant
for all t.
Consider a particular fixed t (that is, a particular point on the curve), the gradient
of f(x, y) at this point (that is, the vector Vf = Vf(x(t,y(t))and the derivative
vector r' = (x'(t), y'(t)).
Which from the statements below is true?
A The angle between vectors Vf and r' may be equal to any angle between 0 and T.
Vectors Vƒ and r' are orthogonal.
(Vectors Vƒ and r' have the same direction.

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