For a particular angle theta, the cosine function f(x) = a cos b(theta) has the following values within one cycle of the function. f(0) = 4; f(pi/4) = 0; f(pi/2) = -4; f(3pi/4) = 0; f(pi) = 4 what is the rule for the cosine function? a) y= 2 cos 4 theta b) y= 4 cos 2 theta c) y= -4 cos 3 theta d) y= 1/4cos 2 theta

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0