Explanation Given: The given function is y = x 2 + 1 x − 4 . Calculation: Given:the given interval is [ 5 , 6 ] . Use quotient rule . ( f g ) ' = f ' ⋅ g − g ' ⋅ f g 2 y = x 2 + 1 x − 4 y ' = d d x ( x 2 + 1 ) ⋅ ( x − 4 ) − d d x ( x − 4 ) ⋅ ( x 2 + 1 ) ( x − 4 ) 2 y ' = 2 x ( x − 4 ) − ( x 2 + 1 ) ( x − 4 ) 2 y ' = 2 x 2 − 8 x − x 2 − 1 ( x − 4 ) 2 y ' = x 2 − 8 x − 1 ( x − 4 ) 2 For critical point y ' = 0

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Question

Chapter 4.2, Problem 39E

To determine

Find theminimum and maximum values of the given functionin the given interval by comparing with critical and end points.

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Chapter 4.2, Problem 38E

Chapter 4.2, Problem 40E

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Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?

1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist, state that fact. и (a) f'(-5) (b) f'(-3) (c) f'(0) (d) f'(5) 2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5) = 4. - 3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2) and f'(2).

Does the series converge or diverge

Chapter 4 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

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Prob. 63CRE Ch. 4 - Prob. 64CRE Ch. 4 - Prob. 65CRE Ch. 4 - Prob. 66CRE Ch. 4 - Prob. 67CRE Ch. 4 - Prob. 68CRE Ch. 4 - Prob. 69CRE Ch. 4 - Prob. 70CRE Ch. 4 - Prob. 71CRE Ch. 4 - Prob. 72CRE Ch. 4 - Prob. 73CRE Ch. 4 - Prob. 74CRE Ch. 4 - Prob. 75CRE Ch. 4 - Prob. 76CRE Ch. 4 - Prob. 77CRE Ch. 4 - Prob. 78CRE Ch. 4 - Prob. 79CRE Ch. 4 - Prob. 80CRE Ch. 4 - Prob. 81CRE Ch. 4 - Prob. 82CRE Ch. 4 - Prob. 83CRE Ch. 4 - Prob. 84CRE Ch. 4 - Prob. 85CRE Ch. 4 - Prob. 86CRE Ch. 4 - Prob. 87CRE Ch. 4 - Prob. 88CRE Ch. 4 - Prob. 89CRE

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Find theminimum and maximum values of the given functionin the given interval by comparing with critical and end points.

Solution Summary: The author calculates the minimum and maximum values of the given function by comparing with critical and end points.

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Find theminimum and maximum values of the given functionin the given interval by comparing with critical and end points.

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Chapter 4 Solutions