1. (2 Points) Let f(x) be a function with f (0) = 1 and f'(x) = f(x). Estimate f(1) using tangent line approximation in four steps. This can be done by hand or by using the SageMath cell below Exercise 1 in the online version of the lab. (a) Since f'(0) = f(0) = 1, the tangent line at x = 0 is y - 1 = 1(x - 0) or y = x + 1. Use this to approximate f (4). f ( 1 ) ~ 1.25 (b) Use (a) to determine an approximate tangent line at x = y = 1.25(x-0.25)+1.25 (c) Use the tangent line from part (b) to approximate f (?). f ( 2 ) ~ 1.5625 (d) Repeat the process above to approximate f (?) and f (1). f ( 3 ) ~ 125/64 f (1) ~ 625/256