1. Consider the equation x3 + 4x2. - 10 on the interval [1,2]. (a) (15 pts) Change the equation to the fixed point form x = = g(x) using simple algebraic manipulations. Show that the equation has a unique root in [1,2] by verifying that g(x) satisfies the hypothesis of the Fixed-Point theorem. (b) (10 pts) Using the fixed point form obtained in part (a), find the root of the equation in [1,2]. 2. Let f(x)=sinx. (a) (12 pts) Use the following values and five-digit rounding arithmetic to construct the Hermite interpolating polynomial to approximate f(0.34) = sin 0.34. X f(x) f'(x) 0.30 0.29552 0.95534 0.32 0.31457 0.94924 0.35 0.34290 0.93937 (b) (13 pts) Determine an error bound for the approximation in part (a), and compare it to the actual error.