if the position function of an object is given by a function of time , then the average velocity between and , for is given by:

this is really the formula for the slope between two points disguised, in case you need help remembering it.

for instance, for part (i)

let

then you want:

you want to estimate the slope of a tangent to the curve at 2. in part (a) you kept taking the slope of points between 2 and something increasingly closer to 2. all these slopes get closer and closer to the value of the slope you are looking for. try to guess what these numbers are heading towards, and that is your estimate

b.) Estimate the instantaneous velocity whent=2.

I am totally stuck I am not sure where to start I know. I know have to plug in the various times into the equation they gave. I also know that this problem has something to do wit-av. velocity=change in distance / change in time.

if you have done derivatives already, you can check your answer by finding f ' (2)