(1) (10 points) Find Cubic Splines for the given data: x f(x) 0.1 -0.29004996 0.2 -0.56079734 0.3 -0.81401972 [Every mistake in the theory of the construction of the spline will cost 1 point and each calculation mistake will cost you 0.5 point. To be done by hand (Use of Python is not allowed for this question)] (2) (10 points) The data in (1) was generated using f(x) = xcosx - 3x. Use the cubic splines con- structed in (1) to find errors for f(0.18) and f'(0.18) Finding f(0.18) and f'(0.18) correctly is (1+1), finding values of the spline and its derivative cor- rectly at 0.18 is (1.5+1.5) and finding errors correctly is (2.5+2.5- 1.5 for the correct formula and 1 for the calculation each)