At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Answer:
f(x) = x^3 -2x^2 -3x +7
Step-by-step explanation:
Cubic polynomial regression using your favorite tool (graphing calculator, spreadsheet, or web site) will tell you the interpolating polynomial is ...
f(x) = x^3 -2x^2 -3x +7
_____
You can use Lagrange polynomial interpolation. It gives the function as the sum of four factored cubics:
[tex]f(x)=3\cdot\dfrac{(x-2)(x-3)(x-4)}{(1-2)(1-3)(1-4)}+1\cdot\dfrac{(x-1)(x-3)(x-4)}{(2-1)(2-3)(2-4)}+\\\\\text{ }\qquad7\cdot\dfrac{(x-1)(x-2)(x-4)}{(3-1)(3-2)(3-4)}+27\cdot\dfrac{(x-1)(x-2)(x-3)}{(4-1)(4-2)(4-3)}[/tex]
Or, you can write equations for the coefficients a, b, c, d of ...
ax^3 +bx^2 +cx +d = f(x)
These would be ...
a + b + c + d = 3
8a +4b +2c +d = 1
27a +9b +3c +d = 7
64a +16b +4c +d = 27
Your friendly linear equation solver will tell you ...
(a, b, c, d) = (1, -2, -3, 7) . . . matches the equation shown above
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.