Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points. (1,2),(2,1),(3,3),(6,1)(1,2),(2,1),(3,3),(6,1).

Annette Arroyo 2020-11-09 Answered
Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points. (1,2),(2,1),(3,3),(6,1)(1,2),(2,1),(3,3),(6,1).
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

jlo2niT
Answered 2020-11-10 Author has 96 answers

Step 1
With x1=1,x2=2,x3=3 and x4=6, the Langrange interpolating polynomials give
p1(x)=(xx2)(xx3)(xx4)(x1x2)(x1x3)(x1x4)
=(x2)(x3)(x6)(12)(13)(16)
=(x25x+6)(x6)(1)(2)(5)
=x36x25x2+30x+6x3610

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-06-13
Carla is using the Rational Root Theorem and synthetic division to find real roots of polynomial functions and sketch their graphs. She says she has wasted her time when she tests a possible root and finds a nonzero remainder instead. Do you agree with her statement? Explain your reasoning.
asked 2021-05-08

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 5. Roots of multiplicity 2 at x=3 and x=1, and a root of multiplicity 1 at x=3. y-intercept at (0, 9)

asked 2021-08-02
Graph each polynomial function. f(x)=x4+x33x2x+2
asked 2021-12-21
Consider the following problem: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens? Draw several diagrams illustrating the situation, some with shallow, wide pens and some with deep, n\Rightarrow pens. Find the total areas of these configurations. Does it appear that there is a maximum area? If so estimate it
asked 2021-06-13
Find the quadratic polynomial whose graph passes through the points (0, 0), (-1, 1), and (1, 1).
asked 2021-01-06
Use your knowledge of the graphs of polynomial functions to make a rough sketch of the graph of y=2x3+x25x+2
asked 2021-08-21
Find a nonzero polymonial function. The given zeros are:
a) 0, 1, 9
b) -3, -1, 0, 1, 3