Explanation Given: The function is R ( p ) = 3600 p − 10 p 3 . Formula used: Linear approximation of Δ f : If f is differentiable at x = a and Δ x is small then Δ f ≈ f ′ ( a ) Δ x Where Δ f = f ( a + Δ x ) − f ( a ) . Calculation: Consider the function R ( p ) = 3600 p − 10 p 3 . First, find the value of R ( p ) for p = 9 . R ( 9 ) = 3600 ( 9 ) − 10 ( 9 ) 3 = 32400 − 7290 = 25110 Differentiate the function with respect to x . R ′ ( p ) = 3600 − 10 ( 3 ) p 3 − 1 = 3600 − 30 p 2 Find the value of Δ R when p is raised by 0.5. Now, apply the linear approximation with a = 9 and Δ p = 0.5 . Use the formula: Δ R ≈ R ′ ( a ) Δ p Δ R ≈ R ′ ( a ) Δ p = R ′ ( 9 ) ( 0

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.1, Problem 29E

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Find the value of R(p) for p=9. Also, find the value of ΔR by using linear approximation if p is raised or lowered by 0.5 euros.

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Chapter 4.1, Problem 28E

Chapter 4.1, Problem 30E

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Find the value of R ( p ) for p = 9 . Also, find the value of Δ R by using linear approximation if p is raised or lowered by 0.5 euros.

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Find the value of R(p) for p=9. Also, find the value of ΔR by using linear approximation if p is raised or lowered by 0.5 euros.

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Chapter 4 Solutions