Explanation Approach: To find f x ( x , y ) , differentiate f ( x , y ) with respect to x by holding y , f x ( x , y ) = ∂ ∂ x f ( x , y ) To find f y ( x , y ) , differentiate f ( x , y ) with respect to y by holding x , f y ( x , y ) = ∂ ∂ y f ( x , y ) Calculation: Consider the given function, f ( x , y ) = 2200 + 27 x 3 + 72 x y + 8 y 2 To find f x ( x , y ) , differentiate f ( x , y ) with respect to x by holding y , f x ( x , y ) = ∂ ∂ x ( 2200 + 27 x 3 + 72 x y + 8 y 2 ) = ∂ ∂ x ( 2200 ) + 27 ∂ ∂ x ( x 3 ) + 72 ∂ ∂ x ( x y ) + 8 ∂ ∂ x ( y 2 ) = 27 ( 3 x 2 ) + 72 ( y ) + 8 ( 0 ) = 81 x 2 + 72 y Thus, f x ( x , y ) = 81 x 2 + 72 y . Substitute f x ( x , y ) = 0 in the function f x ( x , y ) = 81 x 2 + 72 y , 81 x 2 + 72 y = 0 9 x 2 + 8 y = 0 Solve for y , y = − 9 8 x 2 To find f y ( x , y ) , differentiate f ( x , y ) with respect to y by holding x ,

2nd Edition

ISBN: 9780321964038

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

Publisher: Pearson Addison Wesley,

See similar textbooks

Videos

Question

Chapter 9.2, Problem 40E

To determine

To find:

The values of x and y such that both fx(x,y)=0 and fy(x,y)=0 for the function f(x,y)=2200+27x3+72xy+8y2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.2, Problem 39E

Chapter 9.2, Problem 41E

Students have asked these similar questions

Calculus lll May I please have the solutions for the following examples? Thank you

Calculus lll May I please have the solutions for the following exercises that are blank? Thank you

The graph of 2(x² + y²)² = 25 (x²-y²), shown in the figure, is a lemniscate of Bernoulli. Find the equation of the tangent line at the point (3,1). -10 Write the expression for the slope in terms of x and y. slope = 4x³ + 4xy2-25x 2 3 4x²y + 4y³ + 25y Write the equation for the line tangent to the point (3,1). LV Q +

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...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The values of x and y such that both f x ( x , y ) = 0 and f y ( x , y ) = 0 for the function f ( x , y ) = 2200 + 27 x 3 + 72 x y + 8 y 2 .

Solution Summary: The author explains how to find f_x(x,y)=0 for the given function.

Videos

To find:

The values of x and y such that both fx(x,y)=0 and fy(x,y)=0 for the function f(x,y)=2200+27x3+72xy+8y2.

Want to see the full answer?

Chapter 9 Solutions

The values of x and y such that both f x ( x , y ) = 0 and f y ( x , y ) = 0 for the function f ( x , y ) = 2200 + 27 x 3 + 72 x y + 8 y 2 .

Solution Summary: The author explains how to find f_x(x,y)=0 for the given function.

Videos

To find: The values of x and y such that both fx(x,y)=0 and fy(x,y)=0 for the function f(x,y)=2200+27x3+72xy+8y2.

Want to see the full answer?

Chapter 9 Solutions

To find:

The values of x and y such that both fx(x,y)=0 and fy(x,y)=0 for the function f(x,y)=2200+27x3+72xy+8y2.