Explanation Given information: The level curves of afunction f ( x , y ) and a path r ( t ) traversed. Formula used: The derivative is the slope of the tangent that is drawn to the curve at the given point. Slope of a line is positive when the line moves in the upward direction from left to right. Slope of a line is negative when the line moves in the downward direction from left to right. When the curve is anticlockwise than the above result will be reversed. Calculation: From the figure, the path r ( t ) is traversed in anti-clockwise direction. Point A : The curve has tangent line parallel to x − axis . So, the slope of a line is 0. Thus, the slope d d t f ( r ( t ) ) = 0 Point B : The tangent at point B moves upward direction from left to right

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

See similar textbooks

Concept explainers

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magn…

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

Chapter 14.5, Problem 3E

To determine

Write the derivative ddtf(r(t)) is positive, negative, or zero at points A−D.

The figure is:

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.5, Problem 2E

Chapter 14.5, Problem 4E

Students have asked these similar questions

Only 100% sure experts solve it correct complete solutions ok

rmine the immediate settlement for points A and B shown in figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth of foundation (DF-0), thickness of layer below footing (H)=20m. 4m B 2m 2m A 2m + 2m 4m

sy = f(x) + + + + + + + + + X 3 4 5 7 8 9 The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem and the Mean Value Theorem for f on the closed interval [0, 9] ? (A A B B C D

Chapter 14 Solutions

Calculus: Early Transcendentals

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Write the derivative d d t f ( r ( t ) ) is positive, negative, or zero at points A − D . The figure is:

Solution Summary: The author explains how the derivative is the slope of the tangent that is drawn to the curve at the given point.

Concept explainers

Write the derivative ddtf(r(t)) is positive, negative, or zero at points A−D.

The figure is:

Want to see the full answer?

Chapter 14 Solutions

Write the derivative d d t f ( r ( t ) ) is positive, negative, or zero at points A − D . The figure is:

Solution Summary: The author explains how the derivative is the slope of the tangent that is drawn to the curve at the given point.

Concept explainers

Write the derivative ddtf(r(t)) is positive, negative, or zero at points A−D. The figure is:

Want to see the full answer?

Chapter 14 Solutions

Write the derivative ddtf(r(t)) is positive, negative, or zero at points A−D.

The figure is: