Question: P ( t ) = f ( t _ ( 0 ) ) + ( t - t _ ( 0 ) ) f [

P(t)=f(t_(0))+(t-t_(0))f[t_(0),t_(1)]+(t-t_(0))(t-t_(1))f[t_(0),t_(1),t_(2)]+dots We will now compute the divided differences. First divided difference: f[t_(0),t_(1)]=(f(t_(1))-f(t_(0)))/(t_(1)-t_(0)) Second divided difference: f[t_(0),t_(1),t_(2)]=(f[t_(1),t_(2)]-f[t_(0),t_(1)])/(t_(2)-t_(0)) Third divided difference: f[t_(0),t_(1),t_(2),t_(3)]=(f[t_(1),t_(2),t_(3)]-f[t_(0),t_(1),t_(2)])/(t_(3)-t_(0)) We will now compute these differences using t_(0)=8,t_(1)=15,t_(2)=21,t_(3)=28.

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