Hello, i will like help with this assignment. please use details and thank you

1. Suppose that f is a function whose domain is R and satises the following properties: 0 f(:c) = 1 whens: 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(3:) = 04594 +03w3 + 62262 + 61.76 + co. Find the values of co, . . . , C4 such that f is everywhere dierentiable. 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 = 2% 1. (1) Show that (59,11) = (1,1) is a solution to this equation. (ii) Find (iii) Find d_m . '19 (m,y)=(1,1) (iv) Find all point(s) satisfying the equation at which there is a vertical tangent line. 3. Consider the function f (56') = e'\" 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 a: = 0 and y = 0. Find the point a. such that the triangle has largest possible area, and justify that the area has been maximized