00:01
In this problem, we are given that the curve passes through the points 0 .9, 1 .14, 2 .17, 3 .24, 4 .41 and 5 .74.
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We are asked to find out the polynomial by making use of the newton's divided difference method.
00:33
So here let us write down the values of x and y.
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So the values of x are 0, 1, 2, 3, 4 and 5.
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The corresponding values of y are 9, 14, 17, 24, 41, 74.
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So first we calculate the first divided difference, that is del y, is given by subtracting consecutive terms.
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So we have 14 minus 9 to be 5.
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Next we have 17 minus 14 which is 3.
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Next we have 24 minus 17 which is 7.
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41 minus 24 which is 17.
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74 minus 41 33.
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Next we calculate the second divided difference.
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So here we subtract 3 and 5 and we divide it by 2.
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So we get negative 2 over 2 which is negative 1.
01:42
Next we get 4 over 2 which is 2.
01:45
Next we get 10 over 2 which is 5...