5.) Moralc at your company has bcen changing over the past five months. Employce

Question

5.) Moralc at your company has bcen changing over the past five months. Employces werc askcd to anonymously rate their level of satisfaction and happiness with their job on a scale from 0 to 10, where 0 was extremely dissatisfied and 10 was extremely satisfied. You did this regularly for six months and found that the function t 17t1 M(t)2 did a pretty good job of showing the trend of the average employee's morale over that time. second derivative test. (b) Find the point of inflection within this time frame and describe its significance within the (c) Graph M, M', and M" in a vertical column and see where the inflection point of M occurs in each graph.

Explanation / Answer

m(t) = (t2+ 17t + 1) / ( t2+1)
m'(t) = [(t2+1) ( 2t+17) - (t2+17t+1) (2t) ] / (t2+1) 2
m'(t) = (17t2 -34t + 17) / (t2+1)2 =0
For maximum value of m(t), m'(t) =0 and m''(t) <0;
if m'(t) =0 then 2t3 + 2t + 17t2 + 17 -2t3 -34t -2t =0
17t2 -34t +17=0
t2 -2t + 1=0
(t-1)2 =0
t=1;
when t=1;
m''(t) = (t2+1) ( 34t-34) - (17t2 -34t + 17) 2(t2+1)(2t) / (t2+1)4
for t=1;
m''(t) = (1+1) (34-34) - (17-34+17)
m''(t) =0;

Thus, for t=1; M(t) attains a maximum value of 19/2 = 9.5

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