HELP ASAP Evaluate each expression. Make sure to show your work (-4) - 44

Solve the problem and then click on the correct graph. y = |x|

Zielflug [23.3K]

Answer:

Attachment is correct graph.

Step-by-step explanation:

We are given a equation of line y=|x|

It is absolute function which gives always positive value.

It's vertex at (0,0). This function will break at (0,0)

It is linear equality.

$f(x)=\left \{ {-x{\ \ \ \ \ \ x$

So, function is break at point x=0

Now we make tale of x and y

x y

-3 3

-2 2

-1 1

0 0

1 1

2 2

3 3

Now we plot the point on graph and join the points to get graph.

Please see the attachment for correct graph.

8 0

3 years ago

Can anybody help plzz?? 65 points

Yakvenalex [24]

Answer:

$\frac{dy}{dx} =\frac{-8}{x^2} +2$

$\frac{d^2y}{dx^2} =\frac{16}{x^3}$

Stationary Points: See below.

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Calculus

Derivative Notation dy/dx

Derivative of a Constant equals 0.

Stationary Points are where the derivative is equal to 0.

1st Derivative Test - Tells us if the function f(x) has relative max or mins. Critical Numbers occur when f'(x) = 0 or f'(x) = undef
2nd Derivative Test - Tells us the function f(x)'s concavity behavior. Possible Points of Inflection/Points of Inflection occur when f"(x) = 0 or f"(x) = undef

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Quotient Rule: $\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

Step 1: Define

$f(x)=\frac{8}{x} +2x$

Step 2: Find 1st Derivative (dy/dx)

Quotient Rule [Basic Power]: $f'(x)=\frac{0(x)-1(8)}{x^2} +2x$
Simplify: $f'(x)=\frac{-8}{x^2} +2x$
Basic Power Rule: $f'(x)=\frac{-8}{x^2} +1 \cdot 2x^{1-1}$
Simplify: $f'(x)=\frac{-8}{x^2} +2$

Step 3: 1st Derivative Test

Set 1st Derivative equal to 0: $0=\frac{-8}{x^2} +2$
Subtract 2 on both sides: $-2=\frac{-8}{x^2}$
Multiply x² on both sides: $-2x^2=-8$
Divide -2 on both sides: $x^2=4$
Square root both sides: $x= \pm 2$

Our Critical Points (stationary points for rel max/min) are -2 and 2.

Step 4: Find 2nd Derivative (d²y/dx²)

Define: $f'(x)=\frac{-8}{x^2} +2$
Quotient Rule [Basic Power]: $f''(x)=\frac{0(x^2)-2x(-8)}{(x^2)^2} +2$
Simplify: $f''(x)=\frac{16}{x^3} +2$
Basic Power Rule: $f''(x)=\frac{16}{x^3}$

Step 5: 2nd Derivative Test

Set 2nd Derivative equal to 0: $0=\frac{16}{x^3}$
Solve for x: $x = 0$

Our Possible Point of Inflection (stationary points for concavity) is 0.

Step 6: Find coordinates

Plug in the C.N and P.P.I into f(x) to find coordinate points.

x = -2

Substitute: $f(-2)=\frac{8}{-2} +2(-2)$
Divide/Multiply: $f(-2)=-4-4$
Subtract: $f(-2)=-8$

x = 2

Substitute: $f(2)=\frac{8}{2} +2(2)$
Divide/Multiply: $f(2)=4 +4$
Add: $f(2)=8$

x = 0

Substitute: $f(0)=\frac{8}{0} +2(0)$
Evaluate: $f(0)=\text{unde} \text{fined}$

Step 7: Identify Behavior

See Attachment.

Point (-2, -8) is a relative max because f'(x) changes signs from + to -.

Point (2, 8) is a relative min because f'(x) changes signs from - to +.

When x = 0, there is a concavity change because f"(x) changes signs from - to +.

3 0

3 years ago

The scale on a drawing of a swimming pool is 1cm=4m. What is the actual length of the pool if it's 10cm long on the drawing

Usimov [2.4K]

1 cm was multiplied by ten, so wee need to do that on the other side too.

1 times 10 = 10 cm, so 4 times 10 = 40 meters,
So your answer is 40 meters. Hope it helps!

4 0

3 years ago

Read 2 more answers

By definition, the determinant equals ad - bc. What is the value of when x = -2 and y = 3? I NEED HELP PLEASE

sergiy2304 [10]

Answer:

Step-by-step explanation:

Taking the determinant of the matrices we will have;

= 4x(5y) - 2x(3y)

= 20xy - 6xy

= 14xy

Given x = -2 and y = 3

Determinant = 14(-2)(3)

Determinant = -28*3

Determinant = -84

4 0

2 years ago

Need help solving this problem

natka813 [3]

Answer:

Part 1: $\frac{11-x}{5}$ or $\frac{11}{5}-\frac{x}{5}$

Part 2: $\frac{9}{5}$

Step-by-step explanation:

To start things off, you must put everything on the opposite side of y so that you only have the y variable left.

In this case, put x onto the other side, making it negative since it's flipped, so you get $5y=11-x$ (since the x is negative you're using subtraction from 11).

Next, divide both sides by 5 to make 5y into y:

$\frac{5y}{5} =\frac{11}{5}-\frac{x}{5}$

$y=\frac{11}{5}-\frac{x}{5}$

Then in this case you turn y=f(x), but the system did it for you, so all you have to put is $\frac{11}{5}-\frac{x}{5}$ .

For the second part you must replace x with 2 since you need to find f(2).

$\frac{11-2}{5}$

Your answer for part 2 is $\frac{9}{5}$ .

3 0

2 years ago

HELP ASAP Evaluate each expression. Make sure to show your work (-4) - 44 - (-1)