Question 989780
The displacement (in feet) of a particle moving in a straight line is given by s=1/2t^2-6t+23, 

a)Find the average velocity over each time interval a) [4,8], b) [6,8], c) [8,10] d) [8,12]
I'll assume you mean s= (1/2)t^2 - 6t+23
Find the value of x for t = 4, 6, 8, 10 & 12.
s(4) = 7
s(8) = 7
Avg[4,8} = (7-7)/(8-4) = 0
Do the others the same way.
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b)Find the instantaneous velocity when t=8
Find the 1st derivative
s'(t) = t - 6
s'(8) = 8-6 = 2 ft/sec (assuming t is in seconds)
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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).
Plot the points on the graph, etc.
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