G mylab.pearson.com FE C + Survey of Calculus : 24/SP : MAT-1400-DS21 : 45166 denike le roux E Quiz: Quiz 7 Chapter 3 (Sections 3.1-3) Question 10 of 18 This quiz: 18 point(s) possible This question: 1 point(s) possible Submit quiz K Use calculus to prove that the relative minimum or maximum for any function f, as shown below, occurs at x = b Question list 2a f(x) = ax + bx + c, a#0 O Question 10 Where will the relative minimum or maximum for the function occur? Question 11 O an inflection point O a critical value O Question 12 Determine the derivative of the function f(x) = ax + bx + c. f' ( x ) = 0 Question 13 Determine the critical values of f(x) = ax + bx + c. A critical value can occur where f'(x) = 0 and also where f'(x) does not exist. Since f'(x) is a polynomial, there are no x-values where f'(x) does not exist. Therefore, the only critical values will be where f' (x) = 0. Solve the equation f (x) = 0 for x. O Question 14 x=] Prove that x = - - is a maximum or a minimum. Determine f" (x). Question 15 1"' ( x ) = 0 O Question 16 Since f"(x) = 2a is a constant, if a 0, 2a > 0 and f is concave up for all x and x = 2a - is a minimum. O Question 17 Question 18 Time Remaining: 02:27:04 Next@ mylab.pearson.com Survey of Calculus : 24/SP : MAT-1400-DS21: 45166 denike le roux = Quiz: Quiz 7 Chapter 3 (Sections 3.1-3) Question 16 of 18 This quiz: 18 point(s) possible @ This question: 1 point(s) possible LT Question list [ O Question 10 @ Question 11 @ Question 12 @ Question 13 @ Question 14 @ Question 15 O Question 16 O Question 17 @ Question 18 3512 (t+3? Suppose that the value V of the inventory at Fido's Pet Supply, in thousands of dollars, decreases (depreciates) after t months, where V(t)=50 - a) Find V(0), V(5), V(20), and V(60). b) Find the maximum value of the inventory over the interval [0,00). c) Sketch a graph of V. d) Does there seem to be a value below which V(t) will never fall? Explain. a)V(0)= v (Round to two decimal places as needed.) V(5)= V| (Round to two decimal places as needed.) V(20)= V| (Round to two decimal places as needed.) V(60) = V| (Round to two decimal places as needed.) b) To find the maximum value of the inventory over the interval [0,00), it is useful to find the derivative of V(t). Find V'(t). V/(t)= The maximum value of V(t) over the interval [0,00) is (Round to two decimal places as needed.) c) Choose the correct graph below. 0ic: ob. of & o & Q Q > 10+ > Time Remaining: 02:26:54 m @ mylab.pearson.com Survey of Calculus : 24/SP : MAT-1400-DS21: 45166 denike le roux P e - . ; This quiz: 18 point(s) possible - ; = Quiz: Quiz 7 Chapter 3 (Sections 3.1-3) (T TR X R S R B s S LR T 2 Question llSt | Suppose that the value V of the inventory at Fido's Pet Supply, in thousands of dollars, decreases (depreciates) after t months, where V/(t)=50 - ) 35;2)2 . t+ a) Find V(0), V(5), V(20), and V(60). b) Find the maximum value of the inventory over the interval [0,00). O Question 10 c) Sketch a graph of V. d) Does there seem to be a value below which V(t) will never fall? Explain. @ Question 11 OA Oc. Ob. GOAV Q AOA\\'l Q GOAV Q @ Question 12 Q ,+V, [ Q X a \\ i : [ : o1, o4 ~ .'t> = b=, (& @ Question 13 0 40 10 60 0 40 d) Does there seem to be a value below which V(t) will never fall? @ Question 14 p (O A. Yes, the largest value V(t) will never fall below is 0 because V(t) is an inventory value, which cannot be negative. . Yes, the largest value V(t) will never fall below is 35. This is because the graph of V(t) has a vertical asymptote at this value. @ Question 15 No, there is not a value below which V(t) will never fall. . Yes, the largest value V(t) will never fall below is 15. This is because the graph of V(t) has a horizontal asymptote at this value. O Question 16 Explain your answer in the previous step. . The store will maintain stock on its shelves for 35 years. O Question 17 . There will always be some goods on the shelves, and the store always has stock valued at least at $15,000. . The store will maintain stock on its shelves for 15 months. @ Question 18 () D. The store might run out of inventory. Time Remaining: 02:26:50 m G mylab.pearson.com FE C + Survey of Calculus : 24/SP : MAT-1400-DS21 : 45166 denike le roux E Quiz: Quiz 7 Chapter 3 (Sections 3.1-3) Question 17 of 18 This quiz: 18 point(s) possible This question: 1 point(s) possible Submit quiz Find the limit, if it exists. Question list K lim 10 x + x X - - 00 O Question 10 Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. Question 11 O A. lim 10 * +X X - - 00 x + 5 - =(Simplify your answer.) O Question 12 O B. The limit does not exist and is neither - co nor + co. Question 13 O Question 14 Question 15 Question 16 O Question 17 Question 18 Time Remaining: 02:26:44 Next