Respuesta :

Space

Answer:

g'(0) = 0

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Algebra I

  • Function Notation

Pre-Calculus

  • Unit Circle

Calculus

  • Derivatives
  • Derivative Notation
  • The derivative of a constant is equal to 0
  • Derivative Property: [tex]\frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
  • Trig Derivative: [tex]\frac{d}{dx} [cos(x)] = -sin(x)[/tex]

Step-by-step explanation:

Step 1: Define

g(x) = 8 - 10cos(x)

x = 0

Step 2: Differentiate

  1. Differentiate [Trig]:                    g'(x) = 0 - 10[-sin(x)]
  2. Simplify Derivative:                   g'(x) = 10sin(x)

Step 3: Evaluate

  1. Substitute in x:                    g'(0) = 10sin(0)
  2. Evaluate Trig:                      g'(0) = 10(0)
  3. Multiply:                               g'(0) = 0