Question

The process of frying food changes its quality, texture, and color, Suppose the total change in color E (which is measured in the form of energy as ki/mo where C is the temperature(in C) and t is the frying time (in minj. Complete parts a through c of blanched potato strips can be estimated by the function below Etc)" 430.11-1047t _ 5sec-002? +002c2 +008α a. what is the value of E prior to cooking? (Assume that C·0) (Type an integer or decimal b. Use this function to estimate the total change in color of a potato strip that has been cooked for 9 minutes at 160c The total change in color ismo Type an integer or a decimal C. Determine the critical point of this function and determine if a maximum, minimum, or saddle point occurs at that point The critical point is at (LC Type an ordered pair, using integers or decimals Round to two decimal places as needed What kind ofpoint is the critical poim? 0 A, A relative minimum A saddle point O C A relative maximm O D. The kind of point cannot be determined

Answer 1

E(t, c) = 430.11 - 10.47t - 5.58 C - 0.02t^2 + 0.02 c^2 + 0.08 ct t = 0, c = 0 E(0, 0) = 430.11 E = 430.11 kg/mol E(g_1/50) = 403.11 - 10.47 times g - 5.58 times 160 - 0.02 times g^2 + 0.02 times (160)^2 + 0.08 times 160 times g = 430.11 - 94.23 - 892.8 - 1.62 + 512 + 115.2 = 68.66 \r\n Total change is 68.66 kg/mol. To find critical point de/dt = -10.47 - 0.04t + 0.08 C dE/dc = -5.58 + 0.04c + 0.08t To find critical point dE/dt & dE/dc = 0 = 0.08C - 0.04t = 10.47 0.04C + 0.08 t = 5.58 1 - 2 x ii 0.08c - 0.04 t = 10.47 -0.08c + 0.16 t = 11.16/-0.20 t = -0.6g t = 3.45 c = 0.08c = 10.47 + 0.04 t c = 10.47 + 0.04 times 3.45/0.08 = 132.6 c = 132.6 (3.45, 132.6) is critical point \r\n Now to check maxima or maximum d6@t/dt^2 = -0.04