Question

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

Answer 1

Answer:

f'(x) = 1

General Formulas and Concepts:

Calculus

• Limit Properties: $\lim_{n \to a} c = c$
• Definition of a Derivative: $f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Step-by-step explanation:

Step 1: Define

f(x) = x + 2

Step 2: Find derivative

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