Explanation Given information: y = e − ( x − a ) 2 b ; local maximum at x = 2 ; points of inflection at x = 1 and x = 3 . Definition used: Points where f ' ( x ) goes from positive to negative, the function has local maximum. A point at which the graph of a function f changes concavity is called an inflection point. At the inflection points, f ' ' is zero or undefined. Calculation: y = e − ( x − a ) 2 b (Given) Differentiating with respect to ‘t’, we get y ' = − 2 ( x − a ) b e − ( x − a ) 2 b To find the critical points, put y ' = 0 ⇒ − 2 ( x − a ) b e − ( x − a ) 2 b = 0 ⇒ ( x − a ) = 0 ( e − ( x − a ) 2 b ≠ 0 ) ⇒ x = a is the critical point. We have y ' > 0 i f x < 0 a n d y ' < 0 i f x > 0 Therefore, y has maximum at x = a . Since, local maximum at x = 2 , a = 2

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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Chapter 4.2, Problem 41P

To determine

To find:

Formula for the function y=e−(x−a)2b for b>0 with a local maximum at x=2

and points of inflection at x=1 and x=3.

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Chapter 4.2, Problem 40P

Chapter 4.3, Problem 1P

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Chapter 4 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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Formula for the function y = e − ( x − a ) 2 b for b > 0 with a local maximum at x = 2 and points of inflection at x = 1 and x = 3 .

Solution Summary: The author explains the formula for the function y=e-raisebox1ex(x-a)2 !

Videos

To find:

Formula for the function y=e−(x−a)2b for b>0 with a local maximum at x=2

and points of inflection at x=1 and x=3.

Want to see the full answer?

Chapter 4 Solutions

Formula for the function y = e − ( x − a ) 2 b for b &gt; 0 with a local maximum at x = 2 and points of inflection at x = 1 and x = 3 .

Solution Summary: The author explains the formula for the function y=e-raisebox1ex(x-a)2 !

Videos

To find: Formula for the function y=e−(x−a)2b for b>0 with a local maximum at x=2 and points of inflection at x=1 and x=3.

Want to see the full answer?

Chapter 4 Solutions

Formula for the function y = e − ( x − a ) 2 b for b > 0 with a local maximum at x = 2 and points of inflection at x = 1 and x = 3 .

To find:

Formula for the function y=e−(x−a)2b for b>0 with a local maximum at x=2

and points of inflection at x=1 and x=3.