Remember that the maximum rate of change of f at a point u is the length of the of the gradient vector evaluate in u, and the direction in which it occurs is in direction of the gradient vector evaluate in u.

The gradient vector of f is

$\triangledown f(x,y)=(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y})=(2yx^{-\frac{1}{2}}, 4\sqrt x)$

Then, the maximum rate of change is $|\triangledown f(4,5)|=|(2*5*4^{-\frac{1}{2}}, 4\sqrt 4)|=|(5,8)|=\sqrt{5^2+8^2}=\sqrt89$ in the direction of (5,8).

4 0

3 years ago

A rectangle has a perimeter of 34 cm and an area of 52 cm2. its length is 5 more than twice its width. write and solve a system

Vsevolod [243]

Width=4cm
length=13cm

3 0

3 years ago

Which is greater 4.221 or 4.022

Ahat [919]

4.221 is greater because of the .221
.022 see

8 0

3 years ago