Understand the derivative as the slope of the tangent line
Visualize the limit definition: f'(x) = lim (f(x+h)−f(x))/h as h→0
See how the secant line approaches the tangent line
Connect derivative sign to increasing/decreasing behavior
Key Equations
\( f'(x) = \lim_{h\to 0}\frac{f(x+h)-f(x)}{h} \)
\( y - f(a) = f'(a)(x - a) \)
\( m_{sec} = \frac{f(a+h)-f(a)}{h} \)
Why It Matters
The derivative is the central concept of calculus — it measures instantaneous rate of change. From velocity in physics to marginal cost in economics, derivatives describe how quantities change at every single point.
Tags
derivativetangent linesecant linelimit definitionAP Calculus AB