Four less than two-fifths of a number is no less than 2

Find the absolute maximum and minimum values of f(x,y)=xy−4x in the region bounded by the x-axis and the parabola y=16−x2.

skad [1K]

Answer:

The absolute maximum and minimum is $20\; \text{and} -20.$

Step-by-step explanation:

We first check the critical points on the interior of the domain using the

first derivative test.

$f_x=y-4=0$

$f_y=x=0$

The only solution to this system of equations is the point (0, 4), which lies in the domain.

$f_{xx}=0, \;f_{yy}=0\; \text{and}\; f_{xy}=-1$

$\Rightarrow f_{xx}f_{yy}-f_{xy}=o-1=-1$

$\therefore (0,4)$ is a saddle point.

Boundary points - $(4,0), (-4,0), (0,16)$

Along boundary $y=16-x^2$

$f=x(16-x^2)-4x$

$=16x-x^3-4x$

$\Rightarrow f^'=16-3x^2-4=0$

$\Rightarrow 3x^2=12$

$\Rightarrow x=\pm2,\;\;y=14$

Values of f(x) at these points.

$\begin{array}{}(4,0)=-16\\(-4,0)=16\\(0,16)=0\\(2,14)=20\\(-2,14)=-20\end{array}$

Therefore, the absolute maximum and minimum is $20\; \text{and} -20.$

6 0

4 years ago

What is the slope of the equation y- 5 = -3x?

umka21 [38]

Answer:

-3/1

Step-by-step explanation:

It's always the x value over the y value, so whatever's in the x

7 0

3 years ago

Read 2 more answers

Will mark brainliest plz help

PtichkaEL [24]

Answer:

A. 5b > 650 + 2.25b; B. 237 brownies

Step-by-step explanation:

A. Set up the inequality

Let b = the number of brownies. Then

Cost = 650 + 2.25b

Sales = 5b

Profit = Sales - Cost

To make a profit, we must have

Sales - Cost > 0 or

5b > 650 + 2.25b

2. Solve the inequality

$\begin{array}{rcl}5b & > & 650 + 2.25b\\2.75b & > & 650\\b & > & \dfrac{650}{2.75}\\\\& > & 236.4\\\end{array}\\\text{Albert can't sell a fraction of a brownie, so b $>$ 237}\\\text{Albert must sell at least $\large \boxed{\textbf{237 brownies}}$ to make a profit.}$