Explanation Given information: The given function is f ( x ) = x 2 + 4 x − 1 . Formula used: The approximate change in function f ( x ) is, Δ [ f ( x ) ] = f ′ ( x ) Δ x (1) Calculation: The value of Δ x in function f ( x ) changes from a = 4 to b = 4.1 . Δ x = b − a = 4.1 − 4 = 0.1 The function is f ( x ) = x 2 + 4 x − 1 . Differentiate above function with respect to x and get the value of f ′ ( x ) . d d x [ f ( x ) ] = d d x ( x 2 + 4 x − 1 ) f ′ ( x ) = ( x − 1 ) ( ( 2 x + 0 ) 2 x 2 + 4 ) − x 2 + 4 ( 1 − 0 ) ( x − 1 ) 2 ( ∵ d ( u / v ) d x = v d u d x − u d v d x v 2 ) = ( 2 x 2 − 2 x 2 x 2 + 4 ) − x 2 + 4 ( x − 1 ) 2 =

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 3.7, Problem 5TE

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To find: The approximate value of the given function.

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If p(t) is the profit I expect my business to earn t years after opening, use functional notation to express my expected profit after 4 years and 4 months.

3. Consider the function p(x) = (2x³ − 4x +3) 6. A. If ƒ(x) = 2x³ — 4x + 3 and g(x) = x6, then function p is equal to exactly one of the following: f og or go f. Which is it? Explain. B. Thinking of function p as the appropriate composition of functions from Part A, apply the chain rule for derivatives to compute an expression for p'(x). C. Using the chain rule for the derivative computation in Part B is much more efficient than distributing out the product of the six polynomials multiplied in the original expression of f, simplifying that result, and then computing the derivative of that simplified result using the technique from Exercise 1A. Explain. (Please do not waste your time performing this beastly computation, just explain why it would be much more computationally intensive than what was done in Part B.

Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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AUTO TRANSMISSIONS .AND FUEL ECONOMY In trying to...Ch. 3.5 - Prob. 32E Ch. 3.5 - Prob. 33E Ch. 3.5 - Prob. 34E Ch. 3.5 - Prob. 35E Ch. 3.5 - Prob. 36E Ch. 3.5 - Prob. 37E Ch. 3.5 - Prob. 38E Ch. 3.5 - Prob. 39E Ch. 3.5 - Prob. 40E Ch. 3.5 - Prob. 41E Ch. 3.5 - Prob. 42E Ch. 3.5 - Prob. 43E Ch. 3.5 - Prob. 44E Ch. 3.5 - Prob. 45E Ch. 3.5 - Prob. 46E Ch. 3.5 - Prob. 47E Ch. 3.5 - Prob. 48E Ch. 3.5 - Prob. 49E Ch. 3.5 - Prob. 50E Ch. 3.5 - Prob. 1TE Ch. 3.5 - Prob. 2TE Ch. 3.5 - Prob. 3TE Ch. 3.5 - Prob. 4TE Ch. 3.5 - In Exercises 1-8, find the value of the second...Ch. 3.5 - Prob. 6TE Ch. 3.5 - Prob. 7TE Ch. 3.5 - Prob. 8TE Ch. 3.6 - Prob. 1CQ Ch. 3.6 - Prob. 2CQ Ch. 3.6 - Prob. 3CQ Ch. 3.6 - Prob. 4CQ Ch. 3.6 - Prob. 1E Ch. 3.6 - Prob. 2E Ch. 3.6 - Prob. 3E Ch. 3.6 - Prob. 4E Ch. 3.6 - Prob. 5E Ch. 3.6 - Prob. 6E Ch. 3.6 - Prob. 7E Ch. 3.6 - Prob. 8E Ch. 3.6 - Prob. 9E Ch. 3.6 - Prob. 10E Ch. 3.6 - Prob. 11E Ch. 3.6 - Prob. 12E Ch. 3.6 - Prob. 13E Ch. 3.6 - Prob. 14E Ch. 3.6 - Prob. 15E Ch. 3.6 - 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Volume of a Cylinder The volume of a...Ch. 3.6 - Prob. 40E Ch. 3.6 - Prob. 41E Ch. 3.6 - Prob. 42E Ch. 3.6 - Prob. 43E Ch. 3.6 - Prob. 44E Ch. 3.6 - Prob. 45E Ch. 3.6 - Prob. 46E Ch. 3.6 - Prob. 47E Ch. 3.6 - PRODUCTION FUNCTION FOR A FURNITURE COMPANY The...Ch. 3.6 - Prob. 49E Ch. 3.6 - Prob. 50E Ch. 3.6 - Prob. 51E Ch. 3.6 - Prob. 52E Ch. 3.6 - Prob. 53E Ch. 3.6 - Prob. 54E Ch. 3.6 - Prob. 55E Ch. 3.6 - Prob. 56E Ch. 3.6 - Prob. 57E Ch. 3.6 - Prob. 58E Ch. 3.6 - Prob. 59E Ch. 3.6 - Prob. 60E Ch. 3.6 - Prob. 61E Ch. 3.6 - Prob. 62E Ch. 3.6 - Prob. 63E Ch. 3.6 - Prob. 64E Ch. 3.6 - Prob. 65E Ch. 3.6 - 66. 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The approximate value of the given function.

Solution Summary: The author explains the approximate value of the function f(x)=sqrtx

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Chapter 3 Solutions