3. (a) Show that the function f (x) = x 3 + x 2 − 2 has a local minimum at x = 0. (Hint: Show that the first derivative is zero and that the second derivative is positive at x = 0.) (b) Expand this function in a Taylor series around the point x = 0, up to the fourth-order term (the term in x 4 ). (c) If we keep terms only to order x 2 , what is the range in x for which our error is less than 10%?