Math 241 - Spring 2024 Banwarth Name as it appears in Canvas: Lab E OSUID: Print and complete this lab (or complete it on your tablet). Then scan and upload it to Gradescope in the corresponding Lab Assignment. Conceptual questions A. Let s(t) be the height in feet of a rocket t seconds after it took off, straight up into the air. Choose the statement that describes what should be done to correctly answer the following question: “When will the rocket have the acceleration 14 ft/sec²?" ○ Find value t so that s'(t) = 14 ○ Evaluate s'(14) ○ Find value t so that s"(t) = 14 ○ Evaluate s" (14) ○ None of the above will correctly answer the question. B. Let s(t) be the height in feet of a rocket t seconds after taking off, straight up into the air. Choose the statement that describes what should be done to correctly answer the following question: “What velocity will the rocket have 3 seconds after take-off? ○ Find value t so that s'(t) = 3 ○ Evaluate s'(3) ○ Find value t so that s" (t) = 3 ○ Evaluate s❞ (3) ○ None of the above will correctly answer the question. Math 241 Lab E Math skills questions Draw a curve on the axes provided that satisfy the given conditions 1.) ƒ(3) > 0; f'(3) > 0; ƒ"(3) > 0 2. f(-2)>0; f'(−2) <0; ƒ"(−2) > 0 4 -3 -2- -1- 4 -3- -2 -1- -6 -5 -3 -2 0 2 3 4 5 6 -6 -4 -3 -2 -1 0 3 4 5 6 -1- -2- -3 -4 -2- -3- --4- -5- -5- 3. f(4) > 0; f'(4) > 0; ƒ"(4) < 0 5. 4. ƒ(−6) > 0; f'(−6) < 0 ; ƒ"(−6) < 0 -3- -2- 1. -6 -5 -4 -3 -2 -1 0 3 4 5 6 -6 -5 -4 -3 -2 -1 0 2 3 4 5 6 -1 -1 -2- -3 -4 -5 -2- -3- -4 5. f(5) < 0; f'(5) < 0; ƒ"(5) > 0 6. ƒ(−4) < 0; f'(-−4) <0; ƒ" (−4) < 0 -5- 4 3. -2- -1- -6 -5 -4 -3 -1 0 5 6 Math 241 Lab E -3- -4 -5- -6 4 -3 -2- -1- -4 -3 -2 -1 0 3 4 5 6 -1- -2- -3- --4- -5 7.) Draw the graph of a function that satisfies the following conditions: lim f(x) = 4 xx f(0) does not exist f(x) is continuous except at x = 0 f'(x) < 0 on (-∞, 0) and (3,6) f'(x) > 0 on (0,3) and (6,∞) ƒ"(x) < 0 on (−∞,0) and (1,4) ƒ''(x) > 0 on (0,1) and (4,∞) -6- -5 + -3- LO 4. -2 Math 241 Lab E -3- -2- -1- 0 0 --1- -2- -3- -4- -2- -5- + -3. -LO 5 .CO 6 7 8. Describe symbolically where the first and second derivatives of the function graphed below are positive and negative, and make symbolic statements about the end behavior of the function. Round to the nearest 0.2 units, and assume the vertical asymptote is at x = 0.6. 4 X -3 -2 f'(x) < 0: 2 гу 10 -1 -2- -5 -6- 1 f'(x) > 0: f'(x) < 0: ƒ"(x) > 0: lim f(x) = lim f(x) = x-x Math 241 Lab E N- 3 Applied questions Return to Hazel Farms from Lab C. 1.) What is the concavity of the revenue function of Hazel Farms? Explain the economics of the concavity. Answer: 2.) For what quantities of hazelnuts are the following true: R(x) < 0 C(x) < 0 R'(x) < 0 C'(x) < 0 R" (x) < 0 C" (x) < 0 π(x) < 0 π'(x) < 0 π" (x) < 0 3.) Elasticity is a concept from economics that applies to demand (it can also describe supply). A demand function is said to be elastic if small changes in price lead to big changes in demand. A demand function is inelastic if changes in price do not have large effects on demand. a.) For each pair of goods, circle the product that you think will have a more elastic demand curve. American Cheese Italian Parmigiano Reggiano Gasoline Biodiesel Nike Air Jordans Shoes (just any kind of shoe) Groceries Fast food Business air travel Vacation air travel Blueberries Hazelnuts Math 241 Lab E