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bulgar [2K]
1 year ago
6

Help help help please homework is killing me right now

Mathematics
1 answer:
Veronika [31]1 year ago
8 0

The domain of a function is the set of input or argument values for which the function is real and defined.

So, for the given function to be defined, we need to find the possible values for which the values of x makes the square root to be positive.

That is;

-9 -5x ≥ 0

Now, let's solve for x

Add 9 to both-side of the equation

-5x ≥ 9

Divide both-side by -5

x ≤ -9/5

Therefore, the domain of the function can be represented in interval notation as: ( - ∞ , -9/5]

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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:

<u>Pre-Algebra</u>

  • Equality Properties

<u>Calculus</u>

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:

<u>Step 1: Define</u>

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

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

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

<u>Step 3: 1st Derivative Test</u>

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

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

<u>Step 4: Find 2nd Derivative (d²y/dx²)</u>

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

<u>Step 5: 2nd Derivative Test</u>

  1. Set 2nd Derivative equal to 0:                    0=\frac{16}{x^3}
  2. Solve for <em>x</em>:                                                    x = 0

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

<u>Step 6: Find coordinates</u>

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

x = -2

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

x = 2

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

x = 0

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

<u>Step 7: Identify Behavior</u>

<em>See Attachment.</em>

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
What’s the answer to this question?
lutik1710 [3]

Answer: B

Step-by-step explanation:

(f+g)(x) means f(x)+g(x). It is saying to add f(x) and g(x). Since we were given f(x) and g(x), we can directly add them together.

(f+g)(x)=4x+2+x²-6                        [combine like terms]

(f+g)(x)=x²+4x-4

Now that we have found (f+g)(x)=x²+4x-4, the answer is B.

6 0
3 years ago
Finish the sequence of 10 numbers 2,27,52
Kay [80]

Step-by-step explanation:

2,27, 52, 77, 105, 130, 155, 180, 205 230, 255, 280, 305

4 0
2 years ago
I need help on my trig can someone help me on the question please and thank you
IRINA_888 [86]

Answer:

210 degrees

Step-by-step explanation:

Convert the problem from radians to degrees using the ratio 180/ and it will give you 210.

6 0
2 years ago
WILL MARK AS BRAINLIEST The graph plots four equations, A, B, C, and D: Line A joins ordered pair negative 6, 16 and 9, negative
butalik [34]
<span>Equation B and Equation C

Hope this helps

Happy Holidays!</span>
7 0
3 years ago
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