Question: For a given set of data points t,..., tn, define the function (t) by T(t) = (t-t)(t-t)... (t - tn) Show that T' (t)

For a given set of data points t,..., tn, define the function (t) by T(t) = (t-t)(t-t)... (t - tn) Show that

For a given set of data points t,..., tn, define the function (t) by T(t) = (t-t)(t-t)... (t - tn) Show that T' (t) = (tj-t)... (tj tj-1)(tj tj+1)... (tj - tn) (b) [15%] Use the result of part (a) to show that the jth Lagrange basis function can be expressed as lj (t) = = (t) (t-tj)' (tj)

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