The function graphed above is: Concave up on the interval{s) ' Concave down on the interval(s) ' There is an inflection point at: ' An optimization specialist studied a factory's existing processes and work-flow to implemented new equipment and updated production processes. After the new equipment and processes were in place, he studied the production and modeled the productivity with the following function: P(t) 2 4t3 + 90f2 -i- 5t, where t is the number of hours worked in a 10-hour shift. Find the point of diminishing returns for this factory, where the second derivative is zero. The point of diminishing returns is at t 2 Question Help: D Post to forum ~. ________ _ 'LJ Let f(a:) = 3:3 + 33:2 45$ + 15. (a) Use the definition of a derivative or the derivative rules to find x) =i i (b) Use the definition of a derivative or the derivative rules to find fix) =i i (c) On what open interval is f increasing? interval of increasing = ' (d) On what open interval is f decreasing? interval of decreasing = ' (e) On what open interval is f concave downward? interval of downward concavity = ' (f) On what open interval is f concave upward? interval of upward concavity = ' Question Help: D Post to forum Let m) = 33:3 2m 5 Use the limit definition of the derivative to calculate the derivative of f: flw) =i i Use the same formula from above to calculate the derivative of this new function (i.e. the second derivative of f )z 1%) =i i Question Help: C Post to forum Let h(t) = 432 -2+-3.2 Then h'(t) is h'(2) is h"(t) is and h"(2) is Question Help: D Post to forumLet h(t) = 4t3-2 21533. Then h'(t) is ' 173(2) is ' h"(t) is ' and h"(2) is ' Question Help: D Post to forum Let x) 2 m4 + 23:3 + 2:1:2 + 33:. Then f'(a:) is ' andf'(5) is ' ms) is [ and f"(5) is ' Question Help: D Post to forum m2+ 102: + 24 5w+20 ' (a) f'(5) =i i Let f(;c) = (b) 1%) =i \ [NOTE: There are two ways to do this problem. The first is the quotient rule. The second is much easier and does not use the quotient rule.] Question Help: D Post to forum If f (ac) = 72 - 5et, find: f'(ac) = f' ( 4 ) = f" (ac) = f" (4) = Question Help: Video D Post to forum