Explanation Given: The cube root of 27 is 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 Calculation: The cube root of 27 is 3. We need to calculate Δ f = f ( 27.2 ) − f ( 27 ) by using linear approximation of Δ f . Let the function be f ( x ) = x 3 . Differentiate the function with respect to x f ′ ( x ) = 1 3 x 2 3 We apply the linear approximation to f ( x ) = x 3 with a = 27 and Δ x = 0

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.1, Problem 7E

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The cube root of 27 is 3. How much larger is the cube root of 27.2? Estimate using the linear approximation.

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Chapter 4.1, Problem 6E

Chapter 4.1, Problem 8E

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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

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The cube root of 27 is 3. How much larger is the cube root of 27.2? Estimate using the linear approximation.

Solution Summary: The author calculates the cube root of 27 using the linear approximation of Delta f.

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The cube root of 27 is 3. How much larger is the cube root of 27.2? Estimate using the linear approximation.

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Chapter 4 Solutions