A position function has the positions listed below.
t 2 4 7 10 12
f(t) 34 98 155 205 271
Approximate the instantaneous velocity at t=5. show work.
If we assume a piecewise linear function then the velocity at t=5 is just (155-98)/(7-4) = 19
If you want a secant to average the speed from t=2 to t=7, you get (155-34)/(7-2) = 10.4
a quadratic approximation using the first 3 points yields
f(t) = -2.6t^2 + 47.6t - 50.8
and you can refine the approximation using your favorite interval.
You don't say much about the tools at your disposal.