Question

[A] Find the third degree polynomial satisfying the following data and find $f(4)$ by using Lagrange's formula: egin{tabular}{c|cccc} $x$ & 1 & 3 & 5 & 7 \ $f(x)$ & 24 & 120 & 336 & 720 \ end{tabular} $L_0(x) = $ \ $L_1(x) = $ \ $L_2(x) = $ \ $L_3(x) = $ \ $f(x) = $ \ $f(4) = $ \ HINT: For $L_i(x)$ type your answer as $((x-a)(x-b)(x-c))/d$ where $a, b, c, d$ are constants.

          [A]
Find the third degree polynomial satisfying the following data and find $f(4)$ by using Lagrange's
formula:
egin{tabular}{c|cccc}
$x$ & 1 & 3 & 5 & 7 \
$f(x)$ & 24 & 120 & 336 & 720 \
end{tabular}
$L_0(x) = $ \
$L_1(x) = $ \
$L_2(x) = $ \
$L_3(x) = $ \
$f(x) = $ \
$f(4) = $ \
HINT: For $L_i(x)$ type your answer as $((x-a)(x-b)(x-c))/d$ where $a, b, c, d$ are constants.

[A]
Find the third degree polynomial satisfying the following data and find f(4) by using Lagrange's
formula:
egintabularc|cccc
x 1 3 5 7 f(x) 24 120 336 720 endtabular
L0(x) = L1(x) = L2(x) = L3(x) = f(x) = f(4) = HINT: For Li(x) type your answer as ((x-a)(x-b)(x-c))/d where a, b, c, d are constants.

Added by Kristina B.

Calculus: Early Transcendentals

William Briggs, Lyle Cochran, Bernard… 3rd Edition

Chapter 1

Instant Answer

Solved by Expert Madhur L

06/22/2023

Step 1

We are given four points: (1, 24), (3, 120), (5, 336), and (7, 720). We need to find a third-degree polynomial that fits these points and then use Lagrange's Interpolation Formula to find the value of this polynomial at x = 4. Show more…

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[A] Find the third degree polynomial satisfying the following data and find f(4) by using Lagrange's formula: x 1 3 5 7 f(x) 24 120 336 720 L0(x) = L1(x) = L2(x) = L3(x) = f(x) = f(4) = HINT: For Li(x) type your answer as ((x - a)(x - b)(x - c))/d where a, b, c, d are constants.