myopenmath.com 0 Question 5 E 0/5 pts '0 3 3 99 (9 Details 2 6 Consider the function at) 2 4.9: i 1 . For 3 this function there are two important intervals: (00, A) and (A, 00) where the function is not defined at A. For each of the following intervals, tell whether f(;L') is increasing or decreasing. (00, A): Select an answer 3 (A, 00) Select an answer 0 Note that this function has no inflection points, but we can still consider its concavity. For each of the following intervals, tell whether f(:1:) is concave up or concave down. (00, A). Select an answer C (14,00) Select an answer 3 Question Help: El Video 8 Message instructor Submit Question 0 Question 6 B 0/5 pts '0 3 8 99 G) Details myopenmath.com 9(32) is Select an answer 0 Select an answer 0 h(.'L') is Select an answer 0 Select an answer 0 k($) i5 Select an answer G Select an answer C Question Help: El Video l3 Message instructor Submit Question . Question _ myopenmath.com Ulml ' 'ar 5 0 Question 11 B 0/5 pts '0 3 8 99 G) Details Consider h(v) 2 101m 128 v2 and use the Second Derivative Test to address the following prompts. Determine the value and location of any local minimum of f. Enter the solution in (1), Mo form. If multiple solutions exist, use a comma-separated list to enter the solutions. 0 It has a local minimum at: :1 O h has no local minimum. Determine the value and location of any local maximum of f. Enter the solution in (v, h(v)) form. If multiple solutions exist, use a comma-separated list to enter the solutions. 0 h has a local maximum at: l: O h has no local maximum. Question Help: 8 Message instructor Submit All Pam 4:35 1 LTE ( 7 myopenmath.com Question 13 0/1 pt 9 3 99 0 Details The airplane lands smoothly. Here f is the plane's altitude just before it touches down. Then Of' (t ) > 0, f" ( t ) 0 Of ( t ) 0 , f" (t ) > 0 Question Help: DDVideo Message instructor Submit Question Question 14 0/1 pt 9 3 99 0 Details The population is growing more slowly. Here f is the population. Then Of' ( 2) 0 Of' ( 2) > 0, f" ( 20 ) > 0 Of' ( 2 ) > 0, f" ( 20 ) 0, f\" 0 O f'> 0, f\"> 0 Question Help: El Video 8 Message instructor Submit Question 0 Question 3 B 0/2 Dts Wits myopenmath.com l I " I l ' O ' 0 Question 6 B 0/5 pts 0 3 8 99 (9 Details Consider the function f(:z:) = 4(:z: 2)2/3. For this function there are two important intervals: (00, A) and (A, 00) where A is a critical number. Ais ] For each of the following intervals, tell whether at) is increasing or decreasing. (00, A): Select an answer 0 (151,00); Select an answer 0 For each of the following intervals, tell whether f(U) is concave up or concave down. (00, A): Select an answer 6 (14,00)! Select an answer 0 Question Help: [3] Video 8 Message instructor Submit Question 0 Question 7 a 0/7 pts '0 3 3 99 6) Details myopenmath.com . Question 9 E 0/5 pts '0 3 3 99 6) Details The graph of the function follows. List the x-coordinates of the critical values (enter DNE if none) Z List the x-coordinates of the inflection points (enter DNE if none) Z List the intervals over which the function is increasing or decreasing (use DNE for any empty intervals) List the intervals over which the function is concave up or concave down (use DNE for any empty intervals) Concave up on :] Concave down on S Question Help: 8 Message instructor Submit Question myopenmath.com . Question 4 B 0/4 pts '0 3 8 99 6) Details For each table below, select whether the table represents a function that is increasing or decreasing, and whether the function is concave up or concave down. f(:13) 15 Select an answer 0 Select an answer 0 9(3)) 18 Select an answer G Select an answer 0 LI...\\ 4:34 1 LTE ( 7 myopenmath.com Submit Question Question 3 0/2 pts 9 3 99 0 Details Determine the signs (positive, negative, or zero) of y = f(ac) (shown in the graph) and f'ac) and f"(x) when x = 3. Q The sign of f(3) is Select an answer The sign of f'(3) is Select an answer The sign of f"(3) is Select an answer Question Help: Video Message instructor Submit Question Question 4 0/4 pts 1 3 99 0 Details For each table below, select whether the table represents a function that is increasing myopenmath.com . Question 10 E 0/4 pts '0 3 3 99 G) Details Consider y) : 4y(15y) and use the Second Derivative Test to address the following prompts. Determine the value and location of any local minimum of f, Enter the solution in (y, f(y)) form. If multiple solutions exist, use a comma-separated list to enter the solutions. 0 f has a local minimum at: l O f has no local minimum. Determine the value and location of any local maximum of f. Enter the solution in (y, f (31)) form. If multiple solutions exist, use a comma-separated list to enter the solutions. 0 f has a local maximum at: l l O f has no local maximum. Question Help: 8 Message instructor Submit All Parts . llncfinn 'H myopenmath.com 0 Question 8 [:4 0/4 pts '0 3 Z 99 (9 Details Given the function 9(33) : 8m3 + 108.332 l 4803;, find the first derivative, g'(:L-). 9'08) =[ Notice that g'(;v) : 0 when a: : 4, that is, 914) = 0- Now, we want to know whether there is a local minimum or local maximum at a: : 4, so we will use the second derivative test. Find the second derivative, 9"(22). 9'13?) =[ l Evaluate g"(4). g"(4) : Based on the sign of this number, does this mean the graph of g(:z:) is concave up or concave down at a: = 4? At a: = 4 the graph of g(m) is A Select an answer v Based on the concavity of 9(33) at :1: : 4, does this mean that there is a local minimum or local maximum at a: : 4? At a: = 74 there iS a local Select an answer 0 Question Hel hm: 1 en essaoe