Advertising Function

The manager of the Footloose sandal company determines that t months after initiating and advertising campaign, S(t) hundred pairs of sandals will be sold, where
S(t)=3/t+2 - 12/(t+2)^2 + 5

(a) Find S'(t) and S"(t)
(b) At what time will sales be maximized? What is the maximum level of sales?
(c) The manager plans to terminate the advertising campaign when the sales rate is minimized. When does this occur? What are the sales level and sales rate at this time?


I got A) Which is:
s'(t)=-3(t-6)/(t+2)^3
s''(t)=6(x-10)/(x=2)^4

b) I found the root of derivative s' and got t=6, I plugged it into the original equation and got 5 1/24....I'm stuck, I don't know what to do next or even if I'm doing it right.

Hi lisa1984wilson,


This is fairly basic calculus. This question just requires a little bit of reading, the minimum "rate of" sales means the minimum of the first derivative of sales so if you find the second derivative equal to zero then you should find the minimum sales ratea


let me know how you go

Jam

Sorry but I'm having trouble with this...its probably so easy that I'm over thinking it but I don't know what to do!

The manager of the Footloose sandal company determines that t months after initiating and advertising campaign, S(t) hundred pairs of sandals will be sold, where
S(t)=3/t+2 - 12/(t+2)^2 + 5

(a) Find S'(t) and S"(t)
(b) At what time will sales be maximized? What is the maximum level of sales?
(c) The manager plans to terminate the advertising campaign when the sales rate is minimized. When does this occur? What are the sales level and sales rate at this time?


I got A) Which is:
s'(t)=-3(t-6)/(t+2)^3
s''(t)=6(x-10)/(x=2)^4

s"(t)=0 when t=10
now you may have heard of sign diagrams these can be useful especially for multiple roots.

so take some value of 0<t<10 and we get a negative value for s"(t) then above 10 and we get a positive value for s"(t) so we know the slope of the
s'(t) function is negative for less than 10 but positive for greater than 10
this gives us an approximately convex shaped graph. therefore we can see the minimum of the rate of sales is at t=10.