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

HELP PLEASE I don’t understand

Furkat [3]

Answer:

4 min

Step-by-step explanation:

if you look at the plot the dot is a 4

6 0

3 years ago

Ezra enjoys gardening.

svlad2 [7]

Answer:

Ezra can plant 8 sunflowers

Step-by-step explanation:

0.7S + 0.5L < 11

0.7S + 0.5(10) < 11

0.7S + 5 < 11

0.7S < 6

6 ÷ 0.7 = 8.5

7 0

3 years ago