Explanation Given information: f ( x ) = a ( x − b ln x ) have a local minimum at the point ( 2 , 5 ) . Definition used: For any function f , a point p in the domain of f where f ' ( p ) = 0 or f ' ( p ) is undefined is called a critical point of the function. Calculation: The minimum for f ( x ) = a ( x − b ln x ) is at the point ( 2 , 5 ) . Then we have the critical values of f . ⇒ f ' ( x ) = 0 f ( x ) = a ( x − b ln x ) (Given) Differentiating with respect to ‘x’, we get f ' ( x ) = a ( 1 − b x ) f ' ( x ) = 0 ⇒ a ( 1 − b x ) = 0 ⇒ ( 1 − b x ) = 0 For ( 2 , 5 ) , 1 − b 2 = 0

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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Question

Chapter 4.1, Problem 51P

To determine

To find:

The valuesa and b so that f(x)=a(x−blnx) have a local minimum at the point (2,5).

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Chapter 4.1, Problem 50P

Chapter 4.1, Problem 52P

Chapter 4 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

Ch. 4.1 - Prob. 1P Ch. 4.1 - Prob. 2P Ch. 4.1 - Prob. 3P Ch. 4.1 - Prob. 4P Ch. 4.1 - Prob. 5P Ch. 4.1 - Prob. 6P Ch. 4.1 - Prob. 7P Ch. 4.1 - Prob. 8P Ch. 4.1 - Prob. 9P Ch. 4.1 - Prob. 10P

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The valuesa and b so that f ( x ) = a ( x − b ln x ) have a local minimum at the point ( 2 , 5 ) .

Solution Summary: The author calculates the minimum value for f(x)=aleft (x-bmathrmlnx) at (2,5).

Videos

To find:

The valuesa and b so that f(x)=a(x−blnx) have a local minimum at the point (2,5).

Want to see the full answer?

Chapter 4 Solutions

The valuesa and b so that f ( x ) = a ( x − b ln x ) have a local minimum at the point ( 2 , 5 ) .

Solution Summary: The author calculates the minimum value for f(x)=aleft (x-bmathrmlnx) at (2,5).

Videos

To find: The valuesa and b so that f(x)=a(x−blnx) have a local minimum at the point (2,5).

Want to see the full answer?

Chapter 4 Solutions

To find:

The valuesa and b so that f(x)=a(x−blnx) have a local minimum at the point (2,5).