Question

Use the definition f ′(x) = h0f(x + h) - f(x)h to find the derivative. f(x)=x+2

Answer 1

f'(x) = 1

General Formulas and Concepts:

Calculus

• Limit Properties:
  `\lim_(n \to a) c = c`
• Definition of a Derivative:
  `f'(x)= \lim_(h \to 0) (f(x+h)-f(x))/(h)`

Explanation:

Step 1: Define

f(x) = x + 2

Step 2: Find derivative

1. Substitute:
   `f'(x)= \lim_(h \to 0) (((x + h) + 2)-(x+2))/(h)`
2. Distribute:
   `f'(x)= \lim_(h \to 0) (x + h + 2-x-2)/(h)`
3. Combine like terms:
   `f'(x)= \lim_(h \to 0) (h)/(h)`
4. Divide:
   `f'(x)= \lim_(h \to 0) 1`
5. Evaluate:
   `f'(x)= 1`