2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

Concept explainers

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

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Question

Chapter 9.CR, Problem 6CR

To determine

The given statement is true or not and give the reason.

Statement: “For a function z=f(x,y), suppose that the point (a,b) has been identified such that fx(a,b)=fy(a,b)=0. We can conclude that a relative maximum or a relative minimum must exist at (a,b)”.

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Chapter 9.CR, Problem 5CR

Chapter 9.CR, Problem 7CR

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Chapter 9 Solutions

Calculus For The Life Sciences

Ch. 9.1 - YOUR TURN For the function in Example 1, find...Ch. 9.1 - Prob. 2YT Ch. 9.1 - Prob. 3YT Ch. 9.1 - EXERCISES Let f(x,y)=2x3y+5.Find the following. a....Ch. 9.1 - Prob. 2E Ch. 9.1 - EXERCISES Let h(x,y)=x2+2y2. Find the following....Ch. 9.1 - EXERCISES Let f(x,y)=9x+5ylogx. Find the...Ch. 9.1 - EXERCISES Let f(x,y)=ex+ln(x+y). Find the...Ch. 9.1 - EXERCISES Let f(x,y)=xex+y. Find the following. a....Ch. 9.1 - EXERCISES Let f(x,y)=xsin(x2y). Find the...

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The given statement is true or not and give the reason. Statement: “For a function z = f ( x , y ) , suppose that the point ( a , b ) has been identified such that f x ( a , b ) = f y ( a , b ) = 0 . We can conclude that a relative maximum or a relative minimum must exist at ( a , b ) ”.

Solution Summary: The author explains that if a function z=f(x,y) is true, the tangent plane at that point is parallel to xy

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The given statement is true or not and give the reason.

Statement: “For a function z=f(x,y), suppose that the point (a,b) has been identified such that fx(a,b)=fy(a,b)=0. We can conclude that a relative maximum or a relative minimum must exist at (a,b)”.

Want to see the full answer?

Chapter 9 Solutions

The given statement is true or not and give the reason. Statement: “For a function z = f ( x , y ) , suppose that the point ( a , b ) has been identified such that f x ( a , b ) = f y ( a , b ) = 0 . We can conclude that a relative maximum or a relative minimum must exist at ( a , b ) ”.

Solution Summary: The author explains that if a function z=f(x,y) is true, the tangent plane at that point is parallel to xy

Concept explainers

Videos

The given statement is true or not and give the reason. Statement: “For a function z=f(x,y), suppose that the point (a,b) has been identified such that fx(a,b)=fy(a,b)=0. We can conclude that a relative maximum or a relative minimum must exist at (a,b)”.

Want to see the full answer?

Chapter 9 Solutions

The given statement is true or not and give the reason.

Statement: “For a function z=f(x,y), suppose that the point (a,b) has been identified such that fx(a,b)=fy(a,b)=0. We can conclude that a relative maximum or a relative minimum must exist at (a,b)”.