Explanation Given information: f ( x , y ) = x e x 2 − y , P = ( 1 , 1 ) Calculation: Since the gradient of function is denoted by ∇ f = 〈 ∂ f ∂ x , ∂ f ∂ y 〉 The given equation f ( x , y ) = x e x 2 − y , Differentiating f with respect to x we get, ∂ f ∂ x = ∂ ∂ x x e x 2 − y ⇒ ∂ f ∂ x = x ∂ ∂ x e x 2 − y + e x 2 − y ∂ ∂ x x ⇒ ∂ f ∂ x = x e x 2 − y ( 2 x − 0 ) + e x 2 − y ( 1 ) ⇒ ∂ f ∂ x = 2 x 2 e x 2 − y + e x 2 − y = e x 2 − y ( 2 x 2 + 1 ) Differentiating f with respect to y we get, ∂ f ∂ y = ∂ ∂ y x e x 2 − y ⇒ ∂ f ∂ y = x ∂ ∂ y e To determine (b) Tocalculate: rate of change of f in the direction ∇ f P . To determine (c) Tocalculate: rate of change of f in the directionof a vector making an angle of 45 o with ∇ f P .

4th Edition

ISBN: 9781319309671

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Videos

Question

Chapter 14.5, Problem 38E

To determine

(a)

Tocalculate:

‖∇fP‖

To determine

(b)

Tocalculate:

rate of change of f in the direction ∇fP.

To determine

(c)

Tocalculate:

rate of change of f in the directionof a vector making an angle of 45o with ∇fP.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.5, Problem 37E

Chapter 14.5, Problem 39E

Students have asked these similar questions

Let f(x, y) = xex²-y and P = (3,9). (a) Calculate || Vƒp||. (b) Find the rate of change of f in the direction Vfp. (c) Find the rate of change of f in the direction of a vector making an angle of 45° with Vfp.

Let f(x, y) = xex - y and P = (9, 81). (a) Calculate || Vfp||- ||Vfel| =| (b) Find the rate of change of f in the direction Vfp. (c) Find the rate of change of f in the direction of a vector making an angle of 45° with Vfp.

Find the maximum rate of change of f(x, y) Maximum rate of change: 2/5 In(x? + y?) at the point (-4, -3) and the direction in which it occurs. Direction (unit vector) in which it occurs: -8/25 -6/25 出)

Chapter 14 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

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) Tocalculate: ‖ ∇ f P ‖

Solution Summary: The author explains that the gradient of function is denoted by f(x,y)=xex

Videos

(a)

Tocalculate:

‖∇fP‖

(b)

Tocalculate:

rate of change of f in the direction ∇fP.

(c)

Tocalculate:

rate of change of f in the directionof a vector making an angle of 45o with ∇fP.

Want to see the full answer?

Chapter 14 Solutions

(a) Tocalculate: ‖ ∇ f P ‖

Solution Summary: The author explains that the gradient of function is denoted by f(x,y)=xex

Videos

(a) Tocalculate: ‖∇fP‖

(b) Tocalculate: rate of change of f in the direction ∇fP.

(c) Tocalculate: rate of change of f in the directionof a vector making an angle of 45o with ∇fP.

Want to see the full answer?

Chapter 14 Solutions

(a)

Tocalculate:

‖∇fP‖

(b)

Tocalculate:

rate of change of f in the direction ∇fP.

(c)

Tocalculate:

rate of change of f in the directionof a vector making an angle of 45o with ∇fP.