Answer:
Point A(9, 3)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
- Coordinates (x, y)
- Functions
- Function Notation
- Terms/Coefficients
- Anything to the 0th power is 1
- Exponential Rule [Rewrite]:
- Exponential Rule [Root Rewrite]:
<u>Calculus</u>
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]:
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<em /><em />
<em /><em />
<em />
<u>Step 2: Differentiate</u>
- [Function] Rewrite [Exponential Rule - Root Rewrite]:
- Basic Power Rule:
- Simplify:
- [Derivative] Rewrite [Exponential Rule - Rewrite]:
- [Derivative] Rewrite [Exponential Rule - Root Rewrite]:
<u>Step 3: Solve</u>
<em>Find coordinates of A.</em>
<em />
<em>x-coordinate</em>
- Substitute in <em>y'</em> [Derivative]:
- [Multiplication Property of Equality] Multiply 2 on both sides:
- [Multiplication Property of Equality] Cross-multiply:
- [Equality Property] Square both sides:
<em>y-coordinate</em>
- Substitute in <em>x</em> [Function]:
- [√Radical] Evaluate:
∴ Coordinates of A is (9, 3).
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e