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

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ISBN: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.5, Problem 3E

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

The figure is:

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Chapter 14.5, Problem 2E

Chapter 14.5, Problem 4E

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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: