Explanation Given information: L ( x , y ) = 8 + 5 x + 7 y Calculation: The function is said to be linear if equation of the tangent plane to the graph of f ( x , y ) at ( a , b ) is z = f ( a , b ) + f x ( a , b ) ( x − a ) + f y ( a , b ) ( y − b ) The given function is L ( x , y ) = 8 + 5 x + 7 y Hence f ( 2 , 3 ) = 8 , f x ( 2 , 3 ) = 5 and f y To determine (b) Tofind: is the linearization of f centered at ( 2 , 3 ) ?

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

See similar textbooks

Videos

Question

Chapter 14.4, Problem 3PQ

To determine

(a)

Tofind:

is the linearization of f centered at (2,3).

To determine

(b)

Tofind:

is the linearization of f centered at (2,3) ?

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 2PQ

Chapter 14.4, Problem 4PQ

Students have asked these similar questions

Q1: A slider in a machine moves along a fixed straight rod. Its distance x cm along the rod is given below for various values of the time. Find the velocity and acceleration of the slider when t = 0.3 seconds. t(seconds) x(cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 30.13 31.62 32.87 33.64 33.95 33.81 33.24 Q2: Using the Runge-Kutta method of fourth order, solve for y atr = 1.2, From dy_2xy +et = dx x²+xc* Take h=0.2. given x = 1, y = 0 Q3:Approximate the solution of the following equation using finite difference method. ly -(1-y= y = x), y(1) = 2 and y(3) = −1 On the interval (1≤x≤3).(taking h=0.5).

Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?

1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist, state that fact. и (a) f'(-5) (b) f'(-3) (c) f'(0) (d) f'(5) 2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5) = 4. - 3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2) and f'(2).

Chapter 14 Solutions

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) Tofind: is the linearization of f centered at ( 2 , 3 ) .

Solution Summary: The author explains that the given equation is not a linearization of f at (2,3).

Videos

(a)

Tofind:

is the linearization of f centered at (2,3).

(b)

Tofind:

is the linearization of f centered at (2,3) ?

Want to see the full answer?

Chapter 14 Solutions

(a) Tofind: is the linearization of f centered at ( 2 , 3 ) .

Solution Summary: The author explains that the given equation is not a linearization of f at (2,3).

Videos

(a) Tofind: is the linearization of f centered at (2,3).

(b) Tofind: is the linearization of f centered at (2,3) ?

Want to see the full answer?

Chapter 14 Solutions

(a)

Tofind:

is the linearization of f centered at (2,3).

(b)

Tofind:

is the linearization of f centered at (2,3) ?