4. Let f be a differentiable function of two variables with f(0, 4) = 0 and Vf(0, 4) = (2, v3). (a) Find the maximum rate of change of f at (0,4) and the unit vector in the direction where it occurs. (b) Find the instantaneous rate of change of f at (0, 4) in the direction of the vector (-1, V3).

4. Let f be a differentiable function of two variables with f(0, 4) = 0 and Vf(0, 4) = (2, v3). (a) Find the maximum rate of change of f at (0,4) and the unit vector in the direction where it occurs. (b) Find the instantaneous rate of change of f at (0, 4) in the direction of the vector (-1, V3).

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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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.

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4. Let f be a differentiable function of two variables with f(0,4) = 0 and Vf(0,4) = (2, v3).
(a) Find the maximum rate of change of f at (0,4) and the unit vector in the direction where
it occurs.
(b) Find the instantaneous rate of change of f at (0,4) in the direction of the vector (-1, v3).

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