Multiple Viewpoints Math Example 3

Solution

1. 1
   Limit viewpoint: $f'(a) = \lim_{h\to 0}\frac{f(a+h)-f(a)}{h}$ — the formal analytic definition.
2. 2
   Slope viewpoint: $f'(a)$ is the slope of the tangent line to the graph of $f$ at $x=a$ — geometric.
3. 3
   Rate of change viewpoint: $f'(a)$ is the instantaneous rate at which $f$ is changing at $a$ — physical/applied.