29. Let f be the function given by f(x) = 1:23". From the values ofx given below, find a value of it so that the slope of the line tangent to the graph of f at [x. f (1)) is equal to (1.2? A. 43.091 B. [L112 C. 0.605 D 1.418 E 4.103 34. Given a function f defined by f (x) = -. For what value of x is the tangent to f parallel to x the secant line joining (1, f (1)) to (5, f (5))? A. 3.389 B. 3.497 C. 3.482 D. 3.504 E. 3.61236. The profit P for a company is P = 100xe* where x is in sales. Use the method of differentials to approximate the change in profit as the production increases from x = 115 to x =120units. A) $53.45 B) $263.25 C) $267.24 D) $8,626.57 E) $8,889.5439. Let f be the function defined by f (x) = x -3x3 +9x-10. Find (f-' (4)) . A. 33 B. 33 C. 42 D. 9 E.44. A particle moves on the x-axis with velocity given by v(t) =3/*-11 +9-2 for -3 co. B. P(t) decreases indefinitely as ( -> 0. C. P(t) increases indefinitely as ( -> 0. D. P(t) decreases, then increases indefinitely as ( -> 90. E. P(t) increases, then decreases indefinitely as ( -> 0. 51. Given the demand curve p = 30e" and the supply curve p = 5+0.02x, find the producer surplus to the nearest dollar when the market is in equilibrium. A) $1,034 B) $2,513 C) $2,642 D) $3,547 E) $6,18966. The demand and supply functions for a particular commodity are given. The demand function is D(x) =-0.3x3 +70 and the supply function is S(x) =0.1x- + x +20 where x is the number of thousands of the commodity that will be demanded (sold). Find the producers' surplus at market equilibrium. A. 116.67 B. 200 C. 283.33 D. 316.67 E. 683.3374. Let R be the region in the first quadrant bounded by the graph of f (x) = v1+ x , from x =1to x =4. Approximate the area of R using 3 right-end rectangles of equal width. A. 8.146 B. 8.167 C. 9.521 D. 6.813 E. 8.135