Explanation Given information: The statement “The surge function has exactly one inflection point, and it is always at a t -value greater than the t -value of the critical point.” 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

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 4, Problem 76SYU

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Chapter 4, Problem 75SYU

Chapter 4, Problem 77SYU

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Chapter 4 Solutions

APPLIED CALCULUS-PRINT COMPANION (LL)

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To indicate: Whether the statement is true or false.

Solution Summary: The author indicates whether the statement is true or false. The surge function has exactly one inflection point, and it is always at a t -value greater than the critical point.