#1 (6 pts) We are given the following information about the function f : 6 ;...

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#1 (6 pts) We are given the following information about the function f : 6 ; f(0) = 2. X+1 (I) We will construct a continuous piece = wise linear function, g, an approximation of f on the interval [0, 3]. (Note: g is an approximation of f, NOT a linear approximation!) f'(x) = (a) On the interval [0, 0.5], g is a linear approximation of the function f at a = 0. Find an expression for g (x), 0 ≤ x ≤ 0.5. g(x) = (b) (i) On the interval [0.5, 1], g is a linear function and its graph is a line whose slope is f' (0.5). Find an expression for g (x), 0.5 ≤x≤ 1. (Note, g is continuous at x = 0.5) g(x) = 0≤x≤ 0.5. " 0.5 ≤ x ≤ 1. (ii) Why do we think that the function g might be a good approximation of the function f on the interval [0.5, 1]? #1 (6 pts) We are given the following information about the function f : 6 ; f(0) = 2. X+1 (I) We will construct a continuous piece = wise linear function, g, an approximation of f on the interval [0, 3]. (Note: g is an approximation of f, NOT a linear approximation!) f'(x) = (a) On the interval [0, 0.5], g is a linear approximation of the function f at a = 0. Find an expression for g (x), 0 ≤ x ≤ 0.5. g(x) = (b) (i) On the interval [0.5, 1], g is a linear function and its graph is a line whose slope is f' (0.5). Find an expression for g (x), 0.5 ≤x≤ 1. (Note, g is continuous at x = 0.5) g(x) = 0≤x≤ 0.5. " 0.5 ≤ x ≤ 1. (ii) Why do we think that the function g might be a good approximation of the function f on the interval [0.5, 1]?