Answer:

General Formulas and Concepts:
<u>Pre-Algebra</u>
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Algebra I</u>
- Exponential Rule [Powering]:

<u>Calculus</u>
Derivatives
Derivative Notation
Derivative of a constant is 0
Implicit Differentiation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
eˣ Derivative: ![\displaystyle \frac{d}{dx}[e^u] = u'e^u](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5Eu%5D%20%3D%20u%27e%5Eu)
Step-by-step explanation:
<u>Step 1: Define</u>

<u>Step 2: Differentiate</u>
- Rewrite [Exponential Rule - Powering]:

- Implicit Differentiation:
![\displaystyle \frac{d}{dx}[e^{2x}] = \frac{d}{dx}[7x + 5y + 3]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B7x%20%2B%205y%20%2B%203%5D)
- [Derivative] eˣ derivative:
![\displaystyle 2e^{2x} = \frac{d}{dx}[7x + 5y + 3]](https://tex.z-dn.net/?f=%5Cdisplaystyle%202e%5E%7B2x%7D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B7x%20%2B%205y%20%2B%203%5D)
- [Derivative] Basic Power Rule:

- [Derivative] Simplify:

- [Derivative] [Subtraction Property of Equality] Subtract 7 on both sides:

- [Derivative] [Division Property of Equality] Divide 5 on both sides:

- [Derivative] Rewrite:

Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives - Implicit Differentiation
Book: College Calculus 10e
Answer:
No
Step-by-step explanation:
The vertex for an absolute value equation is the when the expression inside the absolute symbol equals zero.
when x+5=0, x=-5
so the vertex is at (-5,0)
This isn't really a question of math, but rather memorization. I know from memory that this is -6, and -6 * -6 * -6 = -216.