Let p₁ and q₁ be the first-order Taylor polynomials for f(x) = √x centered at 36 and 49, respectively.

a. Find p₁ and q₁.

b. Complete the following table showing the errors when using p₁ and q₁ to approximate f(x) at x = 37, 39, 41, 43, 45, and 47. Use a calculator to obtain an exact value of f(x).

c. At which points in the table is p₁ a better approximation to f than q₁? Explain this result.

Transcribed Image Text:

|V – p,(x)| |Vx – q1(x)| х 37 39 41 43 45 47