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

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.

Posted Date: 3/14/2013 5:26:47 AM | Location : United States







Related Discussions:- Explain why f must be a di?erentiable function, Assignment Help, Ask Question on Explain why f must be a di?erentiable function, Get Answer, Expert's Help, Explain why f must be a di?erentiable function Discussions

Write discussion on Explain why f must be a di?erentiable function
Your posts are moderated
Related Questions
rectangles 7cm by 4cm

if the sum of lengths of hypotenuse and a side of right triangle are given, prove the area of the triangle is maximum when angle between them is pi/3

The length of the sides of a triangle are 2x + y/2 , 5 x/3 + y + 1/2  and 2/3 x  + 2y + 5/2. If the triangle is equilateral. Find its perimeter. A ns: 2x + y/2 = 4x + y

Rick is order a latest triangular sail for his boat. He needs knowing the area of the sail. Which formula will he use? The area of a triangle is 1/2 times the length of the bas


Brad's class collected 320 cans of food. They boxed them in boxes of 40 cans each. How many boxes did they required? To find the number of boxes required, you should divide the

How will the decimal point move when 245.398 is multiplied by 100? It is moved two places to the right. While multiplying by multiples of 10, the decimal point is moved to the

Rachel had 3.25 quart of ice tea. her family drank 9 cups.How many cups are left

prove that cos(a)/1-sin(a)=tan(45+A/2)