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: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.6, Problem 77E

To determine

Show that $\frac{d θ}{d x}$ is equal to

To determine

b)

Show that the condition $y -$ coordinate of $Q$ $f (x) - x f' (x)$

To determine

c)

Show that the condition $\frac{d θ}{d x} = 0$ is equivalent to

To determine

d)

Conclude that $Δ Q P B a n d Δ Q C P$ are similar triangle

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Chapter 4.6, Problem 76E

Chapter 4.6, Problem 78E

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