1. Given f (x) = - x+3 -find the following: x2 - 2x - 15 . lim f (x) x--3 b. All x-values where f(x) is not continuous c. lim f (x) x-0 2. Let f (x) =x# -8x +15. Find all x-values where the slope of the tangent line is horizontal. Cx + 5, x 5 4. Find Us if s(t) = 2Vi + - -412/3 + 5t-14 5. A toy rocket rises vertically in such a way that t seconds after lift-off, it is 2 h(t)= -12 + 30t feet above the ground. What is the average velocity of the rocket from t =1 to t =30? 6. Find g'(x) if g(x) = 3x5 -2V/xANSWERS 1. a. 1 b. x = -3, x =5 c. 2. X =0, X =-2, X =2 3. C=4 4. s'(t) =t-1/2 _10t-3 _81-1/3 + 5 5. 14.5 feet per second 6. g'(x) = -6x-3+13x-15/2 7. a. 3 b. oo c. -2 d. 2 e. 4 f. 2 g. -4, 0, 3 8. As time increases, the concentration of the drug is approaching zero milligrams. 9. 3 feet/second; 6 feet/second/second 10. a. f'(x) = 2x1/3 +15e-5x +1 dt b. y = 6cos(2t) - 4 sint 11. y =-8x +5 12. -0.06 mg/hour 13. -00 14. XO 15. -1.09 kilograms/hour 16. a. T(8) =101.8 F ; On day 8 the temperature of the person is 101.8 F. b. T'(8) = -0.4 'F per day; On day 8 the temperature of the person is decreasing by 0.4 'F per day. 17. Sales are increasing by 22.9 thousand units per month. 18. -4.468 'F per mph