Explanation Given info: ( b − c ) ( x 2 + ( x f ' ( x ) ) 2 ) − ( b − ( f ( x ) − x f ' ( x ) ) ) ( c − ( f ( x ) − x f ' ( x ) ) ) ( x 2 + ( b − f ( x ) ) 2 ) ( x 2 + ( c − f ( x ) ) 2 ) Formula used: θ ( x ) = tan 1 c − f ( x ) x tan − 1 b − f ( x ) x Calculation: θ ( x ) = tan 1 c − f ( x ) x tan − 1 b − f ( x ) x θ ' ( x ) = b − ( f ( x ) − x f ' ( x ) ) x 2 + ( b − f ( x ) ) 2 − c − ( f ( x ) − x f ' ( x ) ) x 2 + ( c − f ( x ) ) 2 ) = ( b − c ) x 2 − b c + ( b + c ) ( f ( x To determine b) Show that the condition y − coordinate of Q f ( x ) − x f ' ( x ) To determine c) Show that the condition d θ d x = 0 is equivalent to To determine d) Conclude that Δ Q P B a n d Δ Q C P are similar triangle

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 4.6, Problem 77E

To determine

Show that dθdx is equal to

To determine

b)

Show that the condition y− coordinate of Q f(x)−xf'(x)

To determine

c)

Show that the condition dθdx=0 is equivalent to

To determine

d)

Conclude that ΔQPB and ΔQCP are similar triangle

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Chapter 4.6, Problem 76E

Chapter 4.6, Problem 78E

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Chapter 4 Solutions

CALCULUS (CLOTH)

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E Ch. 4.1 - Prob. 11E Ch. 4.1 - Prob. 12E Ch. 4.1 - Prob. 13E Ch. 4.1 - Prob. 14E Ch. 4.1 - Prob. 15E Ch. 4.1 - Prob. 16E Ch. 4.1 - Prob. 17E Ch. 4.1 - Prob. 18E Ch. 4.1 - Prob. 19E Ch. 4.1 - Prob. 20E Ch. 4.1 - Prob. 21E Ch. 4.1 - Prob. 22E Ch. 4.1 - Prob. 23E Ch. 4.1 - Prob. 24E Ch. 4.1 - Prob. 25E Ch. 4.1 - Prob. 26E Ch. 4.1 - Prob. 27E Ch. 4.1 - Prob. 28E Ch. 4.1 - Prob. 29E Ch. 4.1 - Prob. 30E Ch. 4.1 - Prob. 31E Ch. 4.1 - Prob. 32E Ch. 4.1 - Prob. 33E Ch. 4.1 - Prob. 34E Ch. 4.1 - Prob. 35E Ch. 4.1 - Prob. 36E Ch. 4.1 - Prob. 37E Ch. 4.1 - Prob. 38E Ch. 4.1 - Prob. 39E Ch. 4.1 - Prob. 40E Ch. 4.1 - Prob. 41E Ch. 4.1 - Prob. 42E Ch. 4.1 - Prob. 43E Ch. 4.1 - Prob. 44E Ch. 4.1 - Prob. 45E Ch. 4.1 - Prob. 46E Ch. 4.1 - Prob. 47E Ch. 4.1 - Prob. 48E Ch. 4.1 - Prob. 49E Ch. 4.1 - Prob. 50E Ch. 4.1 - Prob. 51E Ch. 4.1 - Prob. 52E Ch. 4.1 - Prob. 53E Ch. 4.1 - Prob. 54E Ch. 4.1 - Prob. 55E Ch. 4.1 - Prob. 56E Ch. 4.1 - 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