please answer the 3 questions and try to explain your answers as much as possible,

Thanks !

Question 1 Let f be a function with domain R, such that f(x) =0 for x 1. 3 -2 -1 2 (a) Define f(x) for x E [-1, 1] so that f is continuous everywhere. (b) Find a, b, c, d so that, if f(x) is defined as f(x) = ax3 + bx2 + cx + d for x E [-1, 1], then f is differentiable and continuous everywhere. Question 2 Consider f(x) = 1/x on (0, co). Show that for any a E (0, co), the triangle formed by the tangent line to f at a and the positive x- and y-axes is constant. y = a Question 3 Let f(x) = 2x3 -3x2 -6x + 2. Find the the equations of all tangent lines to f which are parallel to the line y = 6x. (Express the tangent lines in y = ma + b form.)