This Test: 17 pts possible Show that the function r(8) = 0 + sin 3 - 8 has exactly one zero in the interval ( - 00,00). Rolle's Theorem states that for a function f(x) that is continuous at every point over the closed interval [a,b] and differentiable at every point of its interior (a,b), if f(a) = f(b), then there is at least one number c in (a,b) at which f (c) = 0. Find the derivative of r(8) = 0 + sin? |3 ) -s Can the derivative of r(0) be zero in the interval ( - co,co)? No Yes According to Rolle's Theorem, since the derivative of r(0) is never zero in the interval ( - co,co), there cannot be two points @ - a and 0 - b for which r(a) = r(b) in this interval. In other words, the function r(0) has in the interval (- 00,00). Which theorem can be used to determine whether a function has any zeros in a given closed interval? at most one zero no zeroes O A. Mean value theorem at least one zero B. Intermediate value theorem exactly one zero O C. Extreme value theorem To apply this theorem, evaluate the function r(0) = 0 + sing s at each endpoint of the interval [ - 3x,3x]. r( - 3it) = (Type an exact answer, using a as needed.) ? Click to select your answer(s). MacBook Air 44 F 1 FB 49)) FVZ esc 10 F1 F2 20 F3 888 F4 F5 F7 # 4 5 6 7 8 9 O deler 2 T Y U O P Q W E R F G H K 4 S