Show work

(1 point) Find the 700th derivative of f(x) = xex. Answer: f(700) (x) = (1 point) Suppose / is a one-to-one, differentiable function and its inverse function /"is also differentiable. One can show, using implicit differentiation (do it!), that ()'(x) =- ry-(x)) Find (f-')'(-4) if /(5) = -4 and /'(5) = 3/7. (-Y(-4)= (1 point) The population of mice in Alfred is given by P() = 2986ed, where t is in years since 1986. The rate of change of the population is given by the formula mice/yr. In year 1989 the population changes by approximately mice. In 1989 822321112 mice died, which means that mice were born that year. (1 point) Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is C(x) = 4000 + 3x + .01x3 + .0002x3. a) Find the marginal cost function. (b) Find C'(100). (What does this mean?) (c) Find the cost of manufacturing the 101" pair of jeans. (a) C'(x) = (b) C'(100) = dollars/pair (c) Cost = dollars