Which statement about the function is true? The graph of the function f(x) = -(x+3)(x - 1) is shown
below.
O The function is positive for all real values of x where
x<-1.
6-
O The function is negative for all real values ofx
where
x<-3 and where x>1.
O The function is positive for all real values of x where
x>0.
2
O The function is negative for all real values of x
where
X<-3 or x>-1.
-6
-4
2
4
6
х
-2
-2+
-4
-6
6

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