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1. Suppose that f is a function Whose domain is R and satises the following properties: o f(::) = 1 when I 2 o f(0) = 1. (i) Dene the function f on the interval [2, 2] such that f is everywhere continuous. (ii) Suppose that f must have the form of a quartic polynomial on [ 2, 2]; that is, f(:1:) = 434 + 631:3 + c2332 + 13 + co. Find the values of co, . . . ,C4 such that f is everywhere diemntiable. Note: You may choose to give your answers to 5 decimal places instead of writing them as fractions. 2 2. Consider the equation In my = y_ 1. :r (i) Show that (z, y) = (1, l) is a solution to this equation. (ii) Find Q dz d (iii) Find (13 . \"9 {r.y)=(1,1) (iv) Find all poiut(s) satisfying the equation at which there is a vertical tangent line. (ivy)=(l!1) 3. Consider the function f(:r) = 81 on [0, 2], and a point a E [0, 2]. Consider the triangle formed by the tangent line to f at a, and the lines I = 0 and y = 0. Find the point a such that the triangle has largest possible area, and justify that the area has been maximized