Give an example of the following, or explain why no such example exists. (a) A degree 6 polynomial L ( x ) that is zero at x = 1 , 2 , 3 , 4 , 5 , 6 and equal to 10 at x = 7 . (b) A degree 6 polynomial L ( x ) that is zero at x = 1 , 2 , 3 , 4 , 5 , 6 , equal to 10 at x = 7 , and equal to 70 at x = 8 .
Give an example of the following, or explain why no such example exists. (a) A degree 6 polynomial L ( x ) that is zero at x = 1 , 2 , 3 , 4 , 5 , 6 and equal to 10 at x = 7 . (b) A degree 6 polynomial L ( x ) that is zero at x = 1 , 2 , 3 , 4 , 5 , 6 , equal to 10 at x = 7 , and equal to 70 at x = 8 .
Solution Summary: The author explains how to find out the degree 6 polynomial L(x) that is zero for the given x values.
Give an example of the following, or explain why no such example exists. (a) A degree 6 polynomial
L
(
x
)
that is zero at
x
=
1
,
2
,
3
,
4
,
5
,
6
and equal to
10
at
x
=
7
. (b) A degree 6 polynomial
L
(
x
)
that is zero at
x
=
1
,
2
,
3
,
4
,
5
,
6
, equal to
10
at
x
=
7
, and equal to 70 at
x
=
8
.
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