Cubic interpolating functions, chosen so that second derivatives are zero at endpoints
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Expression 13: "f" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis equals "a" Subscript, 1 , Baseline left parenthesis, "x" minus "x" Subscript, 1 , Baseline , right parenthesis cubed plus "b" Subscript, 1 , Baseline left parenthesis, "x" minus "x" Subscript, 1 , Baseline , right parenthesis plus "y" Subscript, 1 , Baseline left brace, "x" Subscript, 1 , Baseline less than or equal to "x" less than or equal to "x" Subscript, 2 , Baseline , right brace Has graph. To audio trace, press ALT+T.f1x=a1x−x13+b1x−x1+y1x1≤x≤x2
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Expression 14: "f" Subscript, 2 , Baseline left parenthesis, "x" , right parenthesis equals "a" Subscript, 2 , Baseline left parenthesis, "x" minus "x" Subscript, 3 , Baseline , right parenthesis cubed plus "b" Subscript, 2 , Baseline left parenthesis, "x" minus "x" Subscript, 3 , Baseline , right parenthesis plus "y" Subscript, 3 , Baseline left brace, "x" Subscript, 2 , Baseline less than or equal to "x" less than or equal to "x" Subscript, 3 , Baseline , right brace Has graph. To audio trace, press ALT+T.f2x=a2x−x33+b2x−x3+y3x2≤x≤x3