Explanation Average Rate of Change The average rate of change of a function f with respect to x over an interval from x to x + h is given by the formula f ( x + h ) − f ( x ) h Instantaneous Rate of Change Given a function f and the graph of y = f ( x ) , the tangent line at the point ( x , f ( x ) ) is the line that passes through this point with slope lim h → 0 f ( x + h ) − f ( x ) h if this limit exists. The slope of the tangent line is also referred to as the instantaneous rate of change of the function f with respect to x . Calculation: Given: P ( x ) = 50 x − x 2 P ( x + h ) = 50 ( x + h ) − ( x + h ) 2 = 50 x + 50 h − ( x 2 + h 2 + 2 x h ) = 50 x + 50 h − x 2 − h 2 − 2 x h P ( x + h ) − P ( x ) = 50 x + 50 h − x 2 − h 2 − 2 x h − ( 50 x − x 2 ) = 50 x + 50 h − x 2 − h 2 − 2 x h − 50 x + x 2 = 50 h − h 2 − 2 x h

Bundle: Nature Of Mathematics, Loose-leaf Version, 13th + Webassign Printed Access Card For Smith's Nature Of Mathematics, 13th Edition, Single-term

13th Edition

ISBN: 9781337605076

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 18.3, Problem 52PS

To determine

To find:

The rate of change of profit at x=20.

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Chapter 18.3, Problem 51PS

Chapter 18.3, Problem 53PS

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Bundle: Nature Of Mathematics, Loose-leaf Version, 13th + Webassign Printed Access Card For Smith's Nature Of Mathematics, 13th Edition, Single-term

Ch. 18.1 - IN YOUR OWN WORDS What are the three main topics...Ch. 18.1 - Prob. 2PS Ch. 18.1 - Prob. 3PS Ch. 18.1 - IN YOUR OWN WORDS Zenos paradoxes remind us of an...Ch. 18.1 - Prob. 5PS Ch. 18.1 - Consider the sequence 0.4, 0.44, 0.444, 0.4444,,...Ch. 18.1 - Consider the sequence 0.5,0.55,0.555,0.5555,, What...Ch. 18.1 - Consider the sequence 6, 6.6, 6.66, 6.666,, What...Ch. 18.1 - Prob. 9PS Ch. 18.1 - Consider the sequence 0.27, 0.2727, 0.272727,,...

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