MAT 145: Test #2 (Part II: 30 points)

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1 MAT 45: Test # (Part II: 3 points) Part : Calculator OK! Name Calculator Used Score A particle moves along the x axis of a coordinate plane so that its position in relation to the origin, in cm, at time t is s(t) = 3 t3 9 t + 9t 3, t in seconds, t any real number. Use this information for questions 4 8. Please carefully check the units of measure included with your responses! (4-8: 3 pts each) 4. Calculate the velocity function, v(t), at time t seconds. Include units. 5. Calculate the acceleration function, a(t), at time t seconds. Include units. 6. Calculate the instantaneous rate of change of the particle s position at time t = seconds. Include units. 7. Leon stated that the particle was at rest at precisely the time t = 9 seconds. (a) Is Leon correct? ( pt) YES NO (Circle one.) (b) Explain and justify your response using calculus-based evidence. ( pts) 8. At t = second: (a) Describe the particle s behavior with respect to whether it is speeding up, slowing down, or neither. ( pt) (b) Show calculus-based evidence (calculations) to support your decision. Explain and justify your response so that you are clearly connecting your evidence to your conclusions. ( pts) (a) Particle behavior at t = sec (circle one): speeding up slowing down neither (b) Explain and connect: Page of 5

2 Georgette is a statistical analyst at the Better Peanut Butter (BPB) manufacturing plant in Salinas. She has determined that an appropriate model for the cost C, in thousands of dollars, to manufacture k tons of peanut butter at the Salinas plant isc(k) = k. Use this information for questions 9 through. 9. In this context, what is the meaning of C(.5) = ? Include units! (3 pts). Explain the meaning of C!(7) =.546 for this situation. Include units! (3 pts). Graph C(k) on your graphing calculator for k. In box (a), sketch the shape of the curve you see in your adjusted window, and use words/units to label each axes. (3 pts) In box (b), circle one best option. ( pt) (a) Sketch of graph on adjusted calculator window (b) Interpretation As the number of tons of peanut butter produced increases, the cost to make peanut butter at the Salinas plant _?_. (Circle one best option.) (i) increases (ii) decreases (iii) increases then decreases (iv) decreases then increases 5 Page of 5

3 . The graph of y = h(x) is shown here. ((a): pt; (b-i): pt; (b-ii): 3 pts) (a) Which one of the following tables of values best describes the derivative of h, h! x? Circle one table! (A) (B) (C) (D) (E) x h! x x h! x x h! x x h! x x h! x 3 (b) Select ONE of the tables above that you did not select for (a). For that table: (i) Identify that table by letter: A B C D E (Circle one.) (ii) Describe why you did not select that table in part (a). Be specific, clear, and precise! 3 Page 3 of 5

4 BONUS! BONUS! BONUS! [I] State the first name and the last name for each of the two individuals who are credited with creating calculus more than 3 years ago. Spelling will be checked! ( pts) [II] Suzzette graphed the parabola g(x) = 3 x + x and the point P = (, 3). She noticed that there would be two lines that contain point P that would be tangent to her parabola. (a) On the axes here: ( pts) (i) Sketch a graph of this parabola. (ii) Plot and label point P. (iii) Sketch the two tangent lines. (b) Determine an equation for each of the tangent lines described here. Write each equation in the form y = mx + b. Include appropriate evidence to justify your equations. Clearly distinguish which equation goes with which tangent line in your sketch. (3 pts) Page 4 of 5

5 Part I: No Calculators ( points) () (): pt each (no partial credit) Calculus I MAT 45 Test #: 5 points Evaluation Criteria () () 3 pts each: correct and complete algebraic evidence showing determination of derivative; correct format as described (3) 4 pts: correct and complete algebraic evidence showing determination of derivative using the limit definition of derivative; correct format as described Part II: Calculators May Be Used (3 points) (4) (5) 3 pts each: correct functions with appropriate units (6) 3 pts: correct response with appropriate units (7) 3 pts: (a) pt: correct yes/no response; (b) pts: appropriate calculus-based justification (8) 3 pts: (a) pt: correct yes/no response; (b) pts: appropriate calculus-based justification (9) 3 pts: Correct interpretation with correct units () 3 pts: Correct interpretation with correct units () 4 pts: (a) pt: Correct representation of the curve from adjusted calculator window; pts: correct axes labels; (b) pt: correct and appropriate interpretation of the situation that corresponds to the behavior of the function, on the indicated interval. () 5 pts: (a) pt: Correct table selected; (b-i) pt: incorrect table indicated; (b-ii) 3 pts: accurate, clear, and precise description. BONUS: Calculators May Be Used (no penalty, 7 points) Bonus (I) pts: correct names with correct spelling Bonus (II) 5 pts: (a) pts: correct graph with all components, appropriately labeled (b) 3 pts: Correct equations, clearly identified to match part (a) and supporting evidence for determining equations. Page 5 of 5

MAT 145: Test #2 (Part II: 31 points)

MAT 145: Test #2 (Part II: 31 points) Part 2: Calculator OK! Name _ Calculator Used Score Use f (x) = 4x for questions 16 through 18. Express all solutions using exact values. Show appropriate x + 3 evidence