Use definition (2) (p. 135) to find the slope of the line tangent to the graph of f at P.
f(x) = x² - 4; P(2, 0)

Verified step by step guidance

1. Step 1: Recall the definition of the derivative as the slope of the tangent line at a point. The derivative of a function f at a point x = a is given by the limit: \( f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h} \).
2. Step 2: Identify the function and the point of interest. Here, the function is \( f(x) = x^2 - 4 \) and the point P is (2, 0). We need to find \( f'(2) \).
3. Step 3: Substitute \( a = 2 \) into the derivative definition: \( f'(2) = \lim_{h \to 0} \frac{f(2+h) - f(2)}{h} \).
4. Step 4: Calculate \( f(2+h) \) and \( f(2) \). We have \( f(2+h) = (2+h)^2 - 4 \) and \( f(2) = 2^2 - 4 \).
5. Step 5: Simplify the expression \( \frac{f(2+h) - f(2)}{h} \) and evaluate the limit as \( h \to 0 \) to find the slope of the tangent line.