Bhuvanish has a favourite continuous odd function g: [-1,1] Rwhich they want to keep a secret. Last night, Bhuvanish was studying a new function f: [-1, 1] R defined by g(t) 15 dt if x [0, 1] 70- +t14 0 g(-t) 70+ t14 if a [-1,0). Bhuvanish knows that f is continuous on [-1, 1] but is unsure about its differentiability on (-1,1). f(x) = - dt (a) Help Bhuvanish justify why f(x) is differentiable for a (-1,0) U (0, 1). Make sure you name all the relevant theorems you used. (b) Do you think that f differentiable at x = 0? Give reasons. Equation Editor A- A-T BIUS X, x Styles Font Size (c) When Harley asked Bhuvanish about their favourite function g, Bhuvanish just gave Harley the function f above and stated that f(x) = -2+ cosh(19x). Equipped with this information, we can deduce that Bhuvanish's favourite function is