MATH 31A Midterm: Math 31A Exam 9
Document Summary
Practice for midterm iia (solutions: (a) use linearization to give an estimate for 3 1017. We rst note that 3 1017 is close to 3 1000 = 10 and so we can use lineariza- tion for the function f (x) = 3 x = x1/3 at x = 1000. Before we start we note that f (x) = 1. L(x) = f (a) + f (a)(x a) We note that f (x) = 2. In particular, at x = 1000 we see that f (x) is negative and so the curve is concave down, i. e. , it is bending down. So we would expect the actual function to be under the tangent line so that the answer in part (a) would be an overestimate. [note: as predicted, but still a good guess. ] For this problem it is good to draw a picture (i recommend you draw one before proceeding with the argument).
