3. estimate the eigenvalues of x" +1(1+t)x = 0, x(0) = x(1) = 0

It takes an ant farm 3 days to consume 1/2 of an apple. at that rate, in how many days will the ant farm consume 3 apples

2. (09.01 lc) a function is shown in the table. x g(x) −3 17 −1 −3 0 −4 2 13 which of the following is a true statement for this function? (5 points) the function is increasing from x = −3 to x = −1. the function is increasing from x = −1 to x = 0. the function is decreasing from x = 0 to x = 2. the function is decreasing from x = −3 to x = −1.

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