Explanation Given: Particle moves along the path y = x 3 unit speed. Given point = ( 2 , 8 ) Formula used: Rate change of angle of inclination is given by | d θ d s | and | d θ d s | = K ( s ) K ( x ) = | f " ( x ) | | 1 + ( f ' ( x ) ) 2 | 3 / 2 Calculation: y = x 3 f ( x ) = x 3 f ' ( x ) = 3 x 2 ( d d x ( x n ) = n x n − 1 ) f " ( x ) = 6 x k ( x ) = | f " ( x ) | | 1 + ( f ' ( x ) ) 2 |

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Chapter 14.4, Problem 72E

To determine

How fast is the tangent turning? $(i .e how fast is the angle of inclination changing)$

When the particle passes through the point $(2, 8)$ ? Where particle moves along the path $y = x^{3}$

With unit speed.

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Chapter 14.4, Problem 71E

Chapter 14.4, Problem 73E

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Chapter 14 Solutions

CALCULUS (CLOTH)

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. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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How fast is the tangent turning? ( i .e how fast is the angle of inclination changing) When the particle passes through the point ( 2 , 8 ) ? Where particle moves along the path y = x 3 With unit speed.

Solution Summary: The author explains how the particle moves along the path y = x 3 unit speed.

Videos

How fast is the tangent turning? $(i .e how fast is the angle of inclination changing)$

When the particle passes through the point $(2, 8)$ ? Where particle moves along the path $y = x^{3}$

With unit speed.

Want to see the full answer?

Chapter 14 Solutions

How fast is the tangent turning? ( i .e how fast is the angle of inclination changing) When the particle passes through the point ( 2 , 8 ) ? Where particle moves along the path y = x 3 With unit speed.

Solution Summary: The author explains how the particle moves along the path y = x 3 unit speed.

Videos

How fast is the tangent turning? (i.e how fast is the angle of inclination changing) When the particle passes through the point (2,8)? Where particle moves along the path y=x3 With unit speed.

Want to see the full answer?

Chapter 14 Solutions

How fast is the tangent turning? $(i .e how fast is the angle of inclination changing)$

When the particle passes through the point $(2, 8)$ ? Where particle moves along the path $y = x^{3}$

With unit speed.