p (x)= −5+ 2 x−3 x2 +2 x3 PART TWO-Can you pleae helo answer these. 2) Then use your polynomial and compute the tangent at the given point a (see below for the groups point) by a) firstly applying the differential quotient and explaining why/how the differential quotient works (this should be again Tutorial like – explain the concept of the derivative based on the differential quotient), b) confirming your result by applying classical differential rules (and again explaining why you used which rules), c) computing the equation of the tangen and d) using again the computer software to illustrate that your computed tangent is indeed a tangent to your polynomial computed in 1) at the given point a. The given points for task: Group 1: A = (-1,-12), B= (2,3) ,C=(1,-4), D=(3,28) a= 1
First set of questions (already answered) can you please help me answer part 2 of the questions? Thanks.
1) First compute the coefficients of a polynomial of degree three
a) plugging in the given points in the general equation of a degree three polynomial leading to a 4 times 4 system of linear equations (with the coefficients of the polynomial as unknows)
The 4 linear system of equations are
a - b + c - d = - 12
a + 2 b + 4 c + 8 d = 3
a + b + c + d = - 4
a + 3 b + 9 c + 27 d = 28 .
b) solving this system with Gauss elimination and using this example to explain how Gauss elimination works in general (this should be really explained in detail/ Tutorial like),
p (x)= −5+ 2 x−3 x2 +2 x3
PART TWO-Can you pleae helo answer these.
2) Then use your polynomial and compute the tangent at the given point a (see below for the groups point) by
a) firstly applying the
b) confirming your result by applying classical differential rules (and again explaining why you used which rules),
c) computing the equation of the tangen and
d) using again the computer software to illustrate that your computed tangent is indeed a tangent to your polynomial computed in 1) at the given point a.
The given points for task:
Group 1:
A = (-1,-12), B= (2,3) ,C=(1,-4), D=(3,28)
a= 1
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