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

Using a number strip substract , Another aid that can help children pract...

Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means

Example of mixing problems, A 1500 gallon tank primarily holds 600 gallons ...

A 1500 gallon tank primarily holds 600 gallons of water along with 5 lbs of salt dissolved into it. Water enters the tank at a rate of 9 gal/hr and the water entering the tank has

What is her commission if she sells a $359, A real estate agent makes a 1.5...

A real estate agent makes a 1.5% commission on her sales. What is her commission if she sells a $359,000 house? Multiply $359,000 by the decimal equivalent of 1.5% (0.015) to ?

Fractions, how do I solve 14/27 - 23/27 =

how do I solve 14/27 - 23/27 =

Geometric progression (g.p.), Learning geometric progression ...

Learning geometric progression vis-á-vis arithmetic progression should make it easier. In geometric progression also we denote the first t

Unitary method, who ,why and when discovered unitary method

who ,why and when discovered unitary method

Are parrellel meet at infinity?, no the parallel lines do not meet at infin...

no the parallel lines do not meet at infinity because the parallel lines never intersect each other even at infinity.if the intersect then it is called perpendicuar lines

Describe adding and subtracting square roots, Describe Adding and Subtracti...

Describe Adding and Subtracting Square Roots? To add or subtract square roots, the radicands must be the same. If the radicands are the same, add/subtract the coefficients (the

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