# Given the function s(t)= -16t2 + 128t, what is the average velocity at time interval [1,2]? Then make a conjecture about the value of the instantaneous velocity at t=1.

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Given the function s(t)= -16t+ 128t, what is the average velocity at time interval [1,2]? Then make a conjecture about the value of the instantaneous velocity at t=1.

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Step 1

The given function is,

Step 2

Compute the average velocity at time interval [1,2] as follows. help_outlineImage TranscriptioncloseAverage velocity at time interval [t,t + h]= S(7 +h)-s(1) (t+h)-t _ Average velocity at time interval [1,21= \$(2)-s(1) 2 1 - 192-112 -80 fullscreen
Step 3

Obtain the instantaneous velocity a... help_outlineImage TranscriptioncloseInstantaneous velocity at t is s'(t)=-321 128 Instantaneous velocity at 1 is s'(1) =96 S fullscreen

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### Derivative 