Practice Test:1. Determine the absolute maximum and minimum of 4 2( ) 2 5f x x x   on the interval – 2  x  1 .Given the demand function .q p=- +27 300:2. Find the elasticity n of the demand function . 3.4 2. E(p) = 3. Determine if it is elastic, inelastic, or of unit elasticity at p = 7. 3. _______________4. A company needs to lease copiers. The copiers can make 1000 copies per hour. The monthly cost to lease the copiers is $80/machine. The operating cost is $6 per hour. The company estimates that it will make about 160,000 copies per month.[a] Find the cost function C(m) if m = # machines used. 3.5 3. [a] C(m) = ___________b] How many machines should be leased to minimize the cost? [b] ___________4. Plot the graph of a function that has the following characteristics: Increasing for 0 < x < 2.7; decreasing for x > 2.7; x-intercept (1, 0); asymptotes: x = 0, y = 0; maximum at (2.7, 0.4); concave up: x > e1.5; concave down: 0 < x < e1.5; inflection point at (4.5, 0.3) 4.4For #5 – 8, use the function --=+8( )4xf xe: 5. Domain: ________________5. Determine its domain, intercepts, and asymptotes:(Plot the results on the graph in #8.) 4.2, 4.4 Intercepts: ______________ f(0) =( ) ( )�� �-�= =lim limx xf x f xAsymptotes: ______________6. Find the intervals of [a] increase, [b] decrease, and any 6. Increasing: ________________relative extrema. (Plot the results on the graph in #8.)Decreasing: ________________Relative Extrema: __________7. Determine where it is concave up, concave down, and any 7. Concave up: _______________inflection points. (Plot the results on the graph in #8.)Concave down: ___________Inflection points: ___________8. Use the information in #5 - #7 to graph the function. Be sure to show asymptotes,intercepts, and other pertinent points.9. A student’s grandparents want to be sure that their grandchild has $80,000 onwhich to retire in 350 years. How much should they deposit now in a trust that is expected to yield an average of 6% a year compounded continuously? 4.2 9. ___________10. How long will it take money to triple if it is invested at 7% compounded quarterly? 10. ___________4.3 11. Differentiate the function f(x) = ln(4x5 – 3x3 – 5x2 + x) 4.3 11. ___________12. Differentiate the function ( )-=22 54x xf x x e4.3 12. ______________________13. Use logarithmic differentiation to find the derivative of ( )+=-55 11 7xf xx4.313. ______________________14. A business estimates that when x thousand people are employed, its profitwill be P(x) million dollars, where ( )= + -280 3 ln 440xP x x for x > 0. 4.4[a] What level of employment maximizes profit? 14. [a] ___________________[b] What is the maximum profit? [b]