Explanation Given information: The statement “The surge function is always concave down”. The surge function y = a t e − b t increases rapidly and then decreases toward zero with a maximum at t = 1 b . Steps Description y = a t e − b t d y d x = a t ( − b e − b t ) + a e − b t ( 1 ) = a e − b t ( 1 − b t ) Finding first derivative of the given function. a e − b t ( 1 − b t ) = 0 1 − b t = 0 − b t = − 1 − b t − b = − 1 − b ⇒ t = 1 b Critical point found by setting up first derivative to zero

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 4, Problem 73SYU

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Chapter 4, Problem 72SYU

Chapter 4, Problem 74SYU

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Chapter 4 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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To indicate: Whether the statement is true or false.

Solution Summary: The author explains that the statement "The surge function is always concave down" is false.