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Question 1. Suppose that f is a function whose domain is R and satisfies the following properties: . f(x) =0 when x 1 . f(0) = 1. 1. Define the function f on the interval [-1, 1] such that f is everywhere continuous. 2. Suppose that f must have the form of a quartic polynomial on [-1, 1]; that is, f(x) = C424 +C323 +c2x2 +cix+ co. Find the values of co, ..., c4 such that f is everywhere differentiable. Question 2. Consider the function f(x) = 1 - x2 on [-1, 1], and a point a E [-1, 1]. Consider the triangle formed by the tangent line to f at a, and the lines x = 0 and y = 0. Find the points a such that the triangle has an area of exactly ? (1 + a2)