Explanation Given information: The given contour map of f ( x , y ) Calculation: Consider the diagram The term f y is the differentiation of f with respect to y keeping x constant. So, f y = △ f △ y We can find change in f at P as Δ f = 12 − 10 = 2 Similarly change in f at Q as Δ f = 16 − 14 = 2 As the value of function increases we can observe that the change in y is more in case of Q than in P . Hence △ f △ y is larger at P than at Q To determine (b) Toexplain: f x ( x , y ) is decreasing as a function of y ; that is, for any fixed value x = a , f x ( a , y ) is decreasing in y .

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

See similar textbooks

Videos

Question

Chapter 14.3, Problem 49E

To determine

(a)

Toexplain:

fy is larger at P than at Q, and fx is more negative at P than at Q.

To determine

(b)

Toexplain:

fx(x,y) is decreasing as a function of y; that is, for any fixed value x=a, fx(a,y) is decreasing in y.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.3, Problem 48E

Chapter 14.3, Problem 50E

Students have asked these similar questions

After a great deal of experimentation, two college senior physics majors determined that when a bottle of French champagne is shaken several times, held upright, and uncorked, its cork travels according to the function below, where s is its height (in feet) above the ground t seconds after being released. s(t)=-16t² + 30t+3 a. How high will it go? b. How long is it in the air?

+6x²+135x+1) (0≤x≤10). a) Find the number of units The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is given by P(x) = In (-x²+6x² + 135x+ that should be sold in order to maximize the total profit. b) What is the maximum profit?

The fox population in a certain region has an annual growth rate of 8 percent per year. It is estimated that the population in the year 2000 was 22600. (a) Find a function that models the population t years after 2000 (t = 0 for 2000). Your answer is P(t) = (b) Use the function from part (a) to estimate the fox population in the year 2008. Your answer is (the answer should be an integer)

Chapter 14 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

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.

(a) Toexplain: f y is larger at P than at Q , and f x is more negative at P than at Q .

Solution Summary: The author explains that f_y is larger at P than Q. The corresponding value of function increases, resulting in a larger change in the y.

Videos

(a)

Toexplain:

fy is larger at P than at Q, and fx is more negative at P than at Q.

(b)

Toexplain:

fx(x,y) is decreasing as a function of y; that is, for any fixed value x=a, fx(a,y) is decreasing in y.

Want to see the full answer?

Chapter 14 Solutions

(a) Toexplain: f y is larger at P than at Q , and f x is more negative at P than at Q .

Solution Summary: The author explains that f_y is larger at P than Q. The corresponding value of function increases, resulting in a larger change in the y.

Videos

(a) Toexplain: fy is larger at P than at Q, and fx is more negative at P than at Q.

(b) Toexplain: fx(x,y) is decreasing as a function of y; that is, for any fixed value x=a, fx(a,y) is decreasing in y.

Want to see the full answer?

Chapter 14 Solutions

(a)

Toexplain:

fy is larger at P than at Q, and fx is more negative at P than at Q.

(b)

Toexplain:

fx(x,y) is decreasing as a function of y; that is, for any fixed value x=a, fx(a,y) is decreasing in y.