Answer:
Slope of the Curve:
Equation of Tangent Line: y + 3 = -3/2(x + 2)
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
<u>Algebra I</u>
Point-Slope Form: y - y₁ = m(x - x₁)
- x₁ - x coordinate
- y₁ - y coordinate
- m - slope
<u>Calculus</u>
The definition of a derivative is the slope of the tangent line.
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Quotient Rule:
Step-by-step explanation:
<u>Step 1: Define</u>
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<u>Step 2: Take Derivative</u>
- Quotient Rule:
- Multiply:
- Subtract:
<u>Step 3: Find Instantaneous Derivative</u>
- Substitute in <em>x</em>:
- Exponents:
- Simplify:
This value shows the slope of the tangent line at the exact value of x = 2.
- Substitute: y + 3 = -3/2(x + 2)