Explanation Given: The given graph is Calculation: Since f ( x ) is continuous on [-3, 0] and differentiable at (-3, 0). It is clear from the graph that f ( − 3 ) = 0 f ( 0 ) = 4 Now, using the Mean Value Theorem f ' ( c ) = f ( b ) − f ( a ) b − a f ' ( c ) = f ( 0 ) − f ( − 3 ) 0 − ( − 3 ) f ' ( c ) = 4 −</

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.1, Problem 51S

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The reason why the given function ‘f’ satisfies the hypothesis of the Mean Value Theorem on the given interval [a, b] and the values c∈(a,b) which satisfies the conclusion of the Mean Value Theorem

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Chapter 3.1, Problem 50S

Chapter 3.1, Problem 52S

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Suppose that the graph below is the graph of f'(x), the derivative of f(x). Find the locations of all relative extrema, and tell whether each extremum is a relative maximum or minimum. Af'(x) Select the correct choice below and fill in the answer box(es) within your choice. (Simplify your answer. Use a comma to separate answers as needed.) -10 86-4-2 -9- B 10 X G A. The function f(x) has a relative maximum at x= relative minimum at x = and a B. The function f(x) has a relative maximum at x= no relative minimum. and has C. There is not enough information given. D. The function f(x) has a relative minimum at x= no relative maximum. and has E. The function f(x) has no relative extrema.

K Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema. f(x) = 12x+13x 12/13 Select the correct choice below and, if necessary, fill in any answer boxes within your choice. OA. There are no relative maxima. The function has a relative minimum of (Use a comma to separate answers as needed.) OB. There are no relative minima. The function has a relative maximum of (Use a comma to separate answers as needed.) OC. The function has a relative maximum of at x= (Use a comma to separate answers as needed.) OD. There are no relative extrema. at x= at x= and a relative minimum of at x=

K Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema. f(x) = - 2 3 9 -4x+17 Select the correct choice below and, if necessary, fill in any answer boxes within your choice. OA. There are no relative minima. The function has a relative maximum of (Use a comma to separate answers as needed.) OB. There are no relative maxima. The function has a relative minimum of (Use a comma to separate answers as needed.) OC. The function has a relative maximum of at x= (Use a comma to separate answers as needed.) OD. There are no relative extrema. at x= at x= and a relative minimum of at x=

Chapter 3 Solutions

Calculus Combo

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The reason why the given function ‘f’ satisfies the hypothesis of the Mean Value Theorem on the given interval [a, b] and the values c ∈ ( a , b ) which satisfies the conclusion of the Mean Value Theorem

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The reason why the given function ‘f’ satisfies the hypothesis of the Mean Value Theorem on the given interval [a, b] and the values c∈(a,b) which satisfies the conclusion of the Mean Value Theorem

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Chapter 3 Solutions