1 . ROLLE'S THEOREM FOR A PIECEWISE FUNCTION Consider the piecewise-defined function f(x) = if 0

1. ROLLE'S THEOREM FOR A PIECEWISE FUNCTION if o < x < 4 Consider the piecewise-defined function ax2+bx+c if 4 < x S 8 (a) [20 pts] Find thc value; of a, b, and c, so that f satisficxs thc hypotheses of Rolle's Theorem on the interval [O, 8]. b (b) [5 pt.s] Note that the c in this function is not the same as c in Rolle's Theorem. So let's call k the value in Rolle's Theorem. Find the value of k on [O, 8] guaranteed by Rolle's Theorem, at which f'(k) = 0. k