To find the derivative of the function $f(x) = 9x + 11$ using the definition of the derivative, we use the following formula:

$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

Step-by-Step Solution:

1. Find $f(x+h)$: $f(x+h) = 9(x+h) + 11 = 9x + 9h + 11$

2. Substitute into the definition: $f'(x) = \lim_{h \to 0} \frac{(9x + 9h + 11) - (9x + 11)}{h}$ Simplify the numerator: $f'(x) = \lim_{h \to 0} \frac{9x + 9h + 11 - 9x - 11}{h} = \lim_{h \to 0} \frac{9h}{h}$

3. Simplify the expression: $f'(x) = \lim_{h \to 0} 9 = 9$

Thus, the derivative of $f(x) = 9x + 11$ is:

$f'(x) = 9$

Would you like further explanation or details on the concept of derivatives?

Here are 5 related questions to explore:

1. How do you compute the derivative of a quadratic function using the definition?
2. What is the geometric interpretation of the derivative?
3. How is the derivative of a constant function computed?
4. Can the definition of the derivative be used to find second derivatives?
5. How does the derivative relate to the slope of a tangent line at a given point?

Tip: When differentiating linear functions, the derivative is simply the coefficient of $x$ since the rate of change is constant.