x? y?Level curves Consider the paraboloid f(x, y) = 16 -16and the point P on the given level curve of f. Compute the slope of theline tangent to the level curve at P, and verify that the tangent line is4orthogonal to the gradient at that point.f(x, y) = 12; P(2V3, 4)

The equation of paraboloid is We have given That implies,

Answered: x? y? Level curves Consider the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

(1 point) If the gradient of ff is ∇f=2z(i) +x (j) +yx (k) and the point P=(−8,−8,−2) lies on the level surface f(x,y,z)=0 find an equation for the tangent plane to the surface at the point P
The plane y = 1 intersects the surface z = x4 + 6xy - y4 in a certain curve . Find the slope of the tangent line to this curve at the pointP = (1, 1, 6).
The plane y = 1 intersects the surface z = x^4 + 6xy − y^4 in a certain curve. Find the slope of the tangent line to this curve at the point P = (1, 1, 6).
Let f(x,y)=(2)0.5sin(xy) a. Find the gradient of f(1/2,pi/2) b. Use your answer to find the equation of the tangent line (in parametric form) to the level curve f(x,y)=1, at the point (1/2,pi/2) c. Graph the level curve together with the point and the tangent line you found above.
(a) Find the coordinates of the point(s) at which the curve y = x*−2/3 has gradient −1/6
A function is given by f(x, y, z) = x^2 y^3 + sin za) Find the gradient of f at a general pointb) Use the answer to part a, and a simple substitution, in order to find the gradient of f at a point (x, y, z) = (1, 1, 0)c) Use the answer to part b in order to find the linear approximation of f around the point (x, y, z) = (1, 1, 0)
Find the gradient vector of the given function at the given point p. Then find the equation of the tangent plane at p. F(x,y)=x³y+3xy², p=(2,-2)
40. (a) Let f(x, y, z) = x2 + y2 − xyz. Find grad f. (b) Find the equation for the tangent plane to the surface f(x, y, z) = 7 at the point (2, 3, 1).
Ive done part a b and c already question : Given a 2-dimensional function ?(?,?)=4?2+???(??)T(x,y)=4y2+sin(πx) a) find the expression for the partial derivative ∂?∂? = pi*cos(pi*x) b) find the expression for the partial derivative ∂?∂? = 8y c) what position within the triangle region can I find the lowest value of ?(?,?)T(x,y)? =32,0 d) ? e) ?

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

x? y? Level curves Consider the paraboloid f(x, y) = 16 - 16 and the point P on the given level curve of f. Compute the slope of the line tangent to the level curve at P, and verify that the tangent line is 4 orthogonal to the gradient at that point. f(x, y) = 12; P(2V3, 4)