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Answer:

\(f'(x) = 0\)

General Formulas and Concepts:

Algebra I

Functions

  • Function Notation

Calculus

Limits

Differentiation

  • Derivatives
  • Derivative Notation
  • Definition of a Derivative:                                                                             \(\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}\)

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle f(x) = 7\)

Step 2: Differentiate

  1. Substitute in function values [Definition of a Derivative]:                           \(\displaystyle f'(x) = \lim_{h \to 0} \frac{7 - 7}{h}\)
  2. Simplify:                                                                                                         \(\displaystyle f'(x) = \lim_{h \to 0} \frac{0}{h}\)
  3. Evaluate limit:                                                                                                 \(\displaystyle f'(x) = 0\)

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

Unit:  Differentiation

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