<aside> ⚡ Derivative of a function $s(t)$ at the point $t = a$ is defined $s’(a) = lim_{h \to 0} \frac{s(a+h)-s(a)}{h}$

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• Limit of the difference quotient as the size of the interval goes to zero

The tangent line to a function $f(x)$ at a point $x = a$ is the line passing through the point $(a, f(a))$ with slope $f’(a)$. That is $y = f’(a)(x-a) + f(a)$

• Note that the derivative is only the slope of the tangent line, ≠ the equation of the tangent line!