What do we call the financial assistance that a student receives to pay for college that must be repaid, with interest, that add
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Answer:
The <em>equation</em> of the tangent line is given by the following equation:
General Formulas and Concepts:
<u>Algebra I</u>
Point-Slope Form: y - y₁ = m(x - x₁)
- x₁ - x coordinate
- y₁ - y coordinate
- m - slope
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]:
Step-by-step explanation:
*Note:
Recall that the definition of the derivative is the <em>slope of the tangent line</em>.
<u>Step 1: Define</u>
<em>Identify given.</em>
<em />
<u>Step 2: Differentiate</u>
- [Function] Apply Exponential Differentiation [Derivative Rule - Chain Rule]:
- [Derivative] Rewrite [Derivative Rule - Multiplied Constant]:
- [Derivative] Apply Derivative Rule [Derivative Rule - Basic Power Rule]:
<u>Step 3: Find Tangent Slope</u>
- [Derivative] Substitute in <em>x</em> = 1:
- Rewrite:
∴ the slope of the tangent line is equal to .
<u>Step 4: Find Equation</u>
- [Function] Substitute in <em>x</em> = 1:
- Rewrite:
∴ our point is equal to .
Substituting in our variables we found into the point-slope form general equation, we get our final answer of:
∴ we have our final answer.
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Learn more about derivatives: brainly.com/question/27163229
Learn more about calculus: brainly.com/question/23558817
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation