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

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 4.1, Problem 51P

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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

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Chapter 4 Solutions

APPLIED CALCULUS-PRINT COMPANION (LL)

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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).

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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).