Define a separate subroutine for each of the following tasks respectively.
2 answers:
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Answer:
y = -1/24 x³ + 5/12 x² − 35/24 x + 25/12
Explanation:
A cubic has the form:
y = ax³ + bx² + cx + d
Given four points, we can write a system of equations:
1 = a + b + c + d
1/2 = 8a + 4b + 2c + d
1/3 = 27a + 9b + 3c + d
1/4 = 64a + 16b + 4c + d
Solving this algebraically would be time-consuming, but we can use matrices to make it easy.
First, we find the inverse of the coefficient matrix. This is messy to do by hand, so let's use a calculator:
Now we multiply by the solution matrix (again using a calculator):
So the cubic is:
y = -1/24 x³ + 5/12 x² − 35/24 x + 25/12