APPM 1350 Midterm: appm1350fall2014exam2_sol
Document Summary
Fall 2014: for these problems, justify and cite any theorems you have used. (a) (9 pts) verify that the function f (x) = x x. 3 interval [0, 9], then nd all numbers c that satisfy the conclusion of rolle"s theorem. satis es the three hypotheses of rolle"s theorem on the (b) (8 pts) let g be a di erentiable odd function de ned on ( , ). Here we have, f (c) = 0 . < 9 thus, necessarily, c = 9/4. (b)(8 pts) we apply the mean value theorem to g(x) on the interval [ b, b] where b is any positive real number. Note that, by assumption, g(x) is (i) continuous on [ b, b], and (ii) di erentiable on ( b, b), so the mean value. Now note that since g is odd, we have g( b) = g(b) and so g (c) = g(b) g( b)
