Question

Given the data below:

Answer 1

Answer:

5.16

Step-by-step explanation:

Since after x=3, value of y starts decreasing for increasing values of x, let's choose. Also we need to find f(x) for x=3.4

x=3,4,5 and f(x)=7,3,1 to find lagrange polynomial

P(x)= ((x-x2)(x-x3)y1)/((x1-x2)(x1-x3) + ((x-x1)(x-x3)y2)/((x2-x1)(x2-x3) + ((x-x1)(x-x2)y3)/((x3-x1)(x3-x2)

P(x)= ((x-4)(x-5)7)/((3-4)(3-5)) + ((x-3)(x-5)3)/((4-3)(4-5)) + ((x-3)(x-4)1)/((5-3)(5-4))

P(x)= x² -11x+31

P(3.4)= 5.16