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
`(f(b)-f(a))/(b-a)`.

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