2 years ago

1/2x + 6= 3x - 4 Solve the system of equations

1 answer:

5 0

1.Combine multiplied terms into a single fraction

2. Multiply by 1

3. Subtract 6 from both sides of the equation

4.Simplify

5.Subtract 3x from both sides of the equation

6.Simplify

7.Multiply all terms by the same value to eliminate fraction denominators

8.Simplify

9.Divide both sides of the equation by the same term

10.Simplify

Solution:x=4

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Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 4y sqrt (x) , (4, 5) max

liubo4ka [24]

Answer:

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).