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

Net Present Value, A business has the opportunity to expand by purchasing ...

A business has the opportunity to expand by purchasing a machine at a cost of £80,000. The machine has an estimated life of 5 years and is projected to generate a cashflow of £20,0

Application of related rates to economics and business, the wholesale p of ...

the wholesale p of string beans in dollars per bushel and the daily supply x in thousands of bushel,are related by the equation px+6x+7p=5950. if the supply is decreasing at the r

Word problem, A girl has 25 plants in all, 8 of them are tomatos. She has 1...

A girl has 25 plants in all, 8 of them are tomatos. She has 10 more bean plants than pepper plants. How many pepper plants does she have?

Probability - Compound Events, David wants to rent a movie. He wants to wat...

David wants to rent a movie. He wants to watch either a comedy or a drama. The movie rental store has 18 comedies and dramas available for rent. Seven of the movies are comedies, a

Area of a hyperbolic wedge, The unit circle will be parametrized by (cosw, ...

The unit circle will be parametrized by (cosw, sinw). Provide a point on it, the region cut out by circle, the x-axis, and the line from the origin to this point has covered area w

Quotient rule (f/g)'' = (f''g - fg'')/g2, Quotient Rule (f/g)' = (f'g - ...

Quotient Rule (f/g)' = (f'g - fg')/g 2 Here, we can do this by using the definition of the derivative or along with Logarithmic Definition. Proof Here we do the pr

Multistage sampling, Multistage sampling Multistage sampling is similar...

Multistage sampling Multistage sampling is similar to stratified sampling except division is done on geographical/location basis, for illustration a country can be divided into

Operation, What is a characteristic of operation

What is a characteristic of operation

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