1. Use the Intermediate Value Theorem to show that: () Vote=x' - 1 has a solution in the interval (-1, 0). (ii) g(x) = r' tan(x) takes on the value = for some r e (0, # ). 2. Determine the derivatives of the following functions using the definition of the derivative. (i) f(x) = -4x3 + 2x (ii) g(3) = 2r + 3 3. Determine the derivatives of the following functions: (i) g(y) = sec(y) (ii) f(x) = 4x* tan(3x) (iid) "() = vesin(2) cos (2c) (iv) h(m) = cot(2m) + 3m-11 12 + 7 (v) y(=) =