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if f(t) were continious on the interval [-2,1] but youo were only given the function for t=-2,-3/2,-1,-1/2 ..,3/2 and 2, explain how would you apporximate f'(1)

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I'd take f(1.5)-f(0.5)

the slope of the line passing through points near f(1) is probably pretty close to f'(1). As the two surrounding points get closer together, the slope more closely approximates f'(1).
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