The displacement (in feet) of a particle moving in a straight line is given by s − 1/2 t² - 6t + 23, where t is measured in seconds.

(a) Find the average velocity over each time interval:

(i) [4, 8] 

(ii) [6, 8]

(iii) [8, 10] 

(iv) [8, 12]

(b) Find the instantaneous velocity when t = 8.

(c) Draw the graph of s as a function of t and draw the secant lines whose slopes are the average velocities in part (a). Then draw the tangent line whose slope is the instantaneous velocity in part (b).