Explanation Mean value theorem of integration : It states that if f ( x ) is a function continuous over an interval [ a , b ] , then there exists at least one number c , a < c < b such that f ( c ) ( b − a ) = ∫ a b f ( x ) d x f ( c ) = 1 b − a ∫ a b f ( x ) d x = f a v e r a g e Given: f ( x ) = x 3 , Interval = [ 0 , A ] Formula used: average of a function f ( x ) over [ a...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 6.2, Problem 61E

To determine

To find: A value c for the given function $f (x) = x^{3}$ on $[0, A]$ , where $A > 0$ such that $f (c) = M$ . Here $M$ represent the average value of the function. Also state that which theorem guarantees existence of such $c$ .

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Chapter 6.2, Problem 60E

Chapter 6.2, Problem 62E

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Chapter 6 Solutions

Calculus - Standalone book

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

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A value c for the given function f ( x ) = x 3 on [ 0 , A ] , where A > 0 such that f ( c ) = M . Here M represent the average value of the function. Also state that which theorem guarantees existence of such c .

Solution Summary: The author explains the mean value theorem of integration, which states that if f ( x ) is a function continuous over an interval, then there exists at least one number c.

Videos

To find: A value c for the given function $f (x) = x^{3}$ on $[0, A]$ , where $A > 0$ such that $f (c) = M$ . Here $M$ represent the average value of the function. Also state that which theorem guarantees existence of such $c$ .

Want to see the full answer?

Chapter 6 Solutions

A value c for the given function f ( x ) = x 3 on [ 0 , A ] , where A &gt; 0 such that f ( c ) = M . Here M represent the average value of the function. Also state that which theorem guarantees existence of such c .

Solution Summary: The author explains the mean value theorem of integration, which states that if f ( x ) is a function continuous over an interval, then there exists at least one number c.

Videos

To find: A value c for the given function f(x)=x3 on [0,A], where A>0 such that f(c)=M. Here M represent the average value of the function. Also state that which theorem guarantees existence of such c.

Want to see the full answer?

Chapter 6 Solutions

A value c for the given function f ( x ) = x 3 on [ 0 , A ] , where A > 0 such that f ( c ) = M . Here M represent the average value of the function. Also state that which theorem guarantees existence of such c .

To find: A value c for the given function $f (x) = x^{3}$ on $[0, A]$ , where $A > 0$ such that $f (c) = M$ . Here $M$ represent the average value of the function. Also state that which theorem guarantees existence of such $c$ .