Explain why f must be a di?erentiable function, Mathematics

Assignment Help:

Let f : R3 → R be de?ned by:
                                       f(x, y, z) = xy2+ x3z4+ y5z6

a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) .

b) Brie?y explain why f must be a di?erentiable function (you just need to "look" at the equations for the partial derivatives).

c) Find D~uf(2, 1, 1) where ~u is a unit vector in the direction of ~v = h4, 3,-1i .

d) Find an equation for the plane which is tangent to the surface de?ned by

xy2+ x3z4+ y5z6= 11

 at the point (2, 1, 1) .

e) Use di?erentials to approximate the value of f(2.01, 1.02, 0.97) . Use a calculator to
?nd a more accurate value, and compare.


Related Discussions:- Explain why f must be a di?erentiable function

Matrix equation , Hi may i know how to substract the (ID)colum matrix from ...

Hi may i know how to substract the (ID)colum matrix from (K)square matrix as per equation below. E = (K - ID)^-1 S K is m*m matrix I is idntity matrix d is column vector s is col

Prove complement of element in boolean algebra is unique, Prove that, the c...

Prove that, the complement of each element in a Boolean algebra B is unique.     Ans:  Proof: Let I and 0 are the unit and zero elements of B correspondingly. Suppose b and c b

Determine the area of the matting, A circular print is being matted in a sq...

A circular print is being matted in a square frame. If the frame is 18 in by 18 in, and the radius of the print is 7 in, what is the area of the matting? (π = 3.14) a. 477.86 in

Pythagorean theorem, when one side of a triangle is 15cm and the bottom of ...

when one side of a triangle is 15cm and the bottom of the triangle is 12cm what would x be rounded to the nearest tenth?

Linear programming, #question.areas of applications of linear program mes t...

#question.areas of applications of linear program mes to solution to engineering problems.

How to solving one-step equations, How to Solving One-Step Equations? E...

How to Solving One-Step Equations? Equations, where one math operation is acting on the variable, can be solved in one step. The trick is to get the variable x by itself - isol

Help!!!, The equation -2x^2-kx-2=0 has two different real soultions. find t...

The equation -2x^2-kx-2=0 has two different real soultions. find the set of possible values for k.

Help with 7th grade home work, I need help finding a answer of my kids home...

I need help finding a answer of my kids homework because I have no clue.. can you please help me

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd