Depth, h(m) Temperature, T (◦C) 0 19.1 −1 19.1 −2 19 −3 18.8 −4 18.7 −5 18.3 −6 18.2 −7 17.6 −8 11.7 −9 9.9 −10 9.1   We can write temperature as a function of the depth: T(h).   Use appropriate data and divided difference algorithm to construct Newton’s interpolating polynomials of degree one (name it by T1(h)) to approximate the value of the temperature at h = −5 m.

1. To maximize a catch of bass in lake, it is suggested to throw the fishing line to the depth of the The characteristic feature of this area is the sudden change in temperature. The depth vs. temperature data for a lake is given in the table.

We can write temperature as a function of the depth: T(h).

1. Use appropriate data and divided difference algorithm to construct Newton’s interpolating polynomials of degree one (name it by T₁(h)) to approximate the value of the temperature at h = −5 m.

1. Use appropriate data and divided difference algorithm to construct Newton’s interpolating polynomials of degree two (name it by T₂(h)) to approximate the value of the temperature at h = −8.5

1. Use appropriate data and divided difference algorithm to construct Newton’s interpolating polynomials of degree three (name it by T₃(h)) to approximate the value of the temperature at h = −8.5