Question

The position of an object moving along a line is given by the function s(t) = -7t^2 + 21(t). Find the average velocity of the object over the following intervals
The average velocity of the object over the interval​ [1, 1 + ​h] is ?

Answer 1

The average velocity of a continuous function $f(x)$ over an interval $[a,b]$ is given by the difference quotient $\dfrac{f(b)-f(a)}{b-a}$.

So the average velocity for the object here would be $\dfrac{s(1+h)-s(1)}{(1+h)-1}=\dfrac{\bigg(-7(1+h)^2+21(1+h)\bigg)-\bigg(-7+21\bigg)}{(1+h)-1}=\dfrac{-7h^2-13h+14}{h}=-7h-13+\dfrac{14}{h}$