Mathematics, 27.11.2020 20:10 Worldprofessor6252

Can anybody help plzz?? 65 points

Answers: 2

Show answers

Answers

Answer from: Laners0219

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

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

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) = undef2nd 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:

x = 2

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

Add:

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 +.

Answer from: Quest

based on context clues you gave i'm assuming the answer would be c.

Pls on time limit : 3 what does this map portray? a. the direction of wind patterns in italy. c. t

Answer from: Quest

Bis the answer! hope this

Another question on Mathematics

Mathematics, 20.06.2019 18:02

If qrs tuv, which congruences are true by cpctc? check all that apply. a. q u b. rs tu c. qs tv d. qr tu e. s v f. r u

Answers: 2

Answer

Mathematics, 21.06.2019 18:30

The median of a data set is the measure of center that is found by adding the data values and dividing the total by the number of data values that is the value that occurs with the greatest frequency that is the value midway between the maximum and minimum values in the original data set that is the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude

Answers: 3

Answer

Mathematics, 21.06.2019 19:00

Write a function for a rotation 90 degrees counter clockwise about the origin, point 0

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

What expression is equivalent to log3(x+4)

Answers: 1

Answer

You know the right answer?

Can anybody help plzz?? 65 points
...