2. (3 pts total) We know that tangent lines approximations typically get worse the further you go from the point (a, f(a)). However, this is not always the case. In fact, sometimes, the tangent line can even touch the function at more than one point. Recall that the error of a tangent line estimate is E(x) = f(x) f'(a)(x a) f(a) (a) (2 pts) Find a function f and values a |E(o)]. In other words, the error at b is greater than the error at c, even though c is farther away from a. Show why your example works. (b) (1 pt) Which function property do examples from part (a) share? Hint: what property should E(x) satisfy? (c) (bonus 1 pt) As a challenge, find a nonlinear function f and point a such that for the tangent line at a, lim... E(x) = 0. In other words, the tangent line approximation gets even better the further you are from a