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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Think About It In Exercises 19–24, determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function f(x, y) at the critical point (x0, y0).

f x x ( x 0 , y 0 ) = 8 , f y y ( x 0 , y 0 ) = 7 , f x y ( x 0 , y 0 ) = 9

To determine

Whether the function f(x,y) at critical point (x0,y0) has a relative maximum, a relative minimum, a saddle point, or insufficient information to find the nature of the function for fxx(x0,y0)=8, fyy(x0,y0)=7, fxy(x0,y0)=9.

Explanation

Given Information:

The second partial derivative of the function at critical point (x0,y0) are fxx(x0,y0)=8, fyy(x0,y0)=7, fxy(x0,y0)=9.

Consider the equation,

d=fxx(a,b)fyy(a,b)[fxy(a,b)]2

The provided critical point is (x0,y0).

Replace (a,b) by (x0,y0),

d=fxx(x0,y0)fyy(x0,y0)[fxy(x0,y0)]2

The provided second partial derivative of the function at critical point (x0,y0) are fxx(x0,y0)=8, fyy(x0,y0)=7, fxy(x0,y0)=9

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