MATH 336 Midterm: MATH 336 NIU Exam 1ans
Document Summary
Solutions: (10 pts; see p 243 example 6) find the absolute max and min values of f (x) = 5x + 35 f (x) = 5 35x 2 = 5 x2 and setting f (x) = 0 gives x = 7. The only critical point in [1, 5] is x = 7. The total cost of producing x units is given by c(x) = 3000 + 20x. P (x) = r(x) c(x) = x(1000 x) (3000 20x) = x2 + 980x 3000. Setting p (x) = 0 gives the critical point x = 490, and this does produce a maximum since p (x) = 2 means that the graph is concave down for all x. 7: (5 pts for each part) find the derivative of each of these functions. (a) f (x) = e x2+7x (b) f (x) = ln(5x2 7) f (x) = e x2+7x( 2x + 7) f (x) =
