Which of the following is true about this graph

Implicit differentiation Please help

Anvisha [2.4K]

Answer:

$y''(-1) =8$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Factoring

Calculus

Implicit Differentiation

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Product Rule: $\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

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

-xy - 2y = -4

Rate of change of the tangent line at point (-1, 4)

Step 2: Differentiate Pt. 1

Find 1st Derivative

Implicit Differentiation [Product Rule/Basic Power Rule]: $-y - xy' - 2y' = 0$
[Algebra] Isolate y' terms: $-xy' - 2y' = y$
[Algebra] Factor y': $y'(-x - 2) = y$
[Algebra] Isolate y': $y' = \frac{y}{-x-2}$
[Algebra] Rewrite: $y' = \frac{-y}{x+2}$

Step 3: Find y

Define equation: $-xy - 2y = -4$
Factor y: $y(-x - 2) = -4$
Isolate y: $y = \frac{-4}{-x-2}$
Simplify: $y = \frac{4}{x+2}$

Step 4: Rewrite 1st Derivative

[Algebra] Substitute in y: $y' = \frac{-\frac{4}{x+2} }{x+2}$
[Algebra] Simplify: $y' = \frac{-4}{(x+2)^2}$

Step 5: Differentiate Pt. 2

Find 2nd Derivative

Differentiate [Quotient Rule/Basic Power Rule]: $y'' = \frac{0(x+2)^2 - 8 \cdot 2(x + 2) \cdot 1}{[(x + 2)^2]^2}$
[Derivative] Simplify: $y'' = \frac{8}{(x+2)^3}$

Step 6: Find Slope at Given Point

[Algebra] Substitute in x: $y''(-1) = \frac{8}{(-1+2)^3}$
[Algebra] Evaluate: $y''(-1) =8$

6 0

2 years ago

Read 2 more answers

Write a matrix to represent the system of equations.

ioda

Answer:

7 -1 6 | -8

7 -5 7 | 1

0 1 -4 | -5

Step-by-step explanation:

Note that there are four columns in this system, representing the variables x, y and z and constants. So the given matrix pattern is appropriate: It has three columns for the coefficients of x, y and z and one column for the constants.

We need only identify the coefficients and transfer them into the appropriate boxes of the matrix pattern.

We get:

7 -1 6 -8

7 -5 7 1

0 1 -4 -5

7 0

2 years ago

Read 2 more answers

132 days to 125.4 days percent of change

Evgen [1.6K]

Answer:

132 days to 125.4 days percent of change

Step-by-step explanation:

p= N-O/O x 100% where p is the percent change, is the New value and O is

the Old value. We are given the Old value (132) and the New value (125.4) which we can substitute into the formula to calculate the percent change:

p= 125.4-132/132 x 100%

p= -6.6/132 x 100%

p= (-660/132%)

p= -5%

5 0

4 months ago

Read 2 more answers

Can you help with this problem 5×-(14-×)=-30-2×

REY [17]

Answer:

-2

Step-by-step explanation:

First remove parenthesis. Next collect the like terms. Next move terms. Next collect the like terms and calculate. Divide both sides by 8. Your answer is -2

6 0

3 years ago

A carpender buys bolts for 1.18 per pound. The carpenter brought 18.5 lb. of bolts. How much did the bolts cost?

riadik2000 [5.3K]

All you have to do is multiply the two numbers together
1.18 x 18.5 = 21.83

4 0

2 years ago