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

Christais attending the county fair that charges a $12 entry fee. The entry fee includes 10 free rides, but any additional rides

ratelena [41]

Answer:

he saves 3 dollars. its not worth it.

Step-by-step explanation:

you divide 12 by ten getting you 1.2 which you subtract from 1.50 that then multiply that by 10

8 0

2 years ago

F(x)=2x + 1 and g(x) = -3x+4. Find f(x) + g(x)

Aneli [31]

To do this, simply add the 2 functions-as it says:

(2x+1) + (-3x+4)
2x+1-3x-4
-x-3

Your answer is -x-3

5 0

2 years ago

Write the algebraic expression 5 more then the product of 4 and m

melomori [17]

Answer:

4m + 5

Step-by-step explanation:

product of 4 and m: 4m

5 more than the product of 4 and m: 4m + 5

Answer: 4m + 5

5 0

2 years ago