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Answer:

f'(-2.4) ≈ -14

General Formulas and Concepts:
Algebra I

Coordinate Planes

  • Coordinates (x, y)

Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Functions

  • Function Notation

Calculus

Differentiation

  • Derivatives
  • Derivative Notation

Step-by-step explanation:

*Note:

The definition of a derivative is the slope of the tangent line.

Step 1: Define

Identify.

f(-2.4) = -1

f(-1.9) = -8

Step 2: Differentiate

Simply plug in the 2 coordinates into the slope formula to find slope m.

  1. [Derivative] Set up [Slope Formula]:                                                           [tex]\displaystyle f'(-2.4) \approx \frac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]
  2. Substitute in coordinates:                                                                           [tex]\displaystyle f'(-2.4) \approx \frac{-8 - -1}{-1.9 - -2.4}[/tex]
  3. Evaluate:                                                                                                       [tex]\displaystyle f'(-2.4) \approx -14[/tex]

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Learn more about derivatives: https://brainly.com/question/17830594

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

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