Calculus help, derivatives!

The efficiency coefficient (E) of a team measured related to is number of team members (t) can be described by the equation E(t) = 2000 + 108t - 4t^3 T € [1,7].

a) Use calculus to determine the number of team members that produces greatest efficiency

b) What is the maximum efficiency coefficient that can be achieved by the team?

 

a) Take the derivative of this function to get 108-12*(t^2). Set this equal to 0, to get t^2=9. t then must be 3.

b) Now plug in 3 into the original equation. You should get 2216

 

you did it so easy, i had to do 108t - 12t^2
= 12(9-t^2)
= 12(3- t)(3-t)
t= 3, t = -3

but idk how you got t^2=9.

 

108-12t^2=0
12t^2=108
t^2=9

Does that work? We also know that t can't be a negative number

 

How about this one:

The hardness (H) of a temporary glue, h hours after application is given by:

H = 2000 + (H - 7)^3

a) Determine the rate of change of H (dH/dh)

b) what is the rate of change of H when h= 0?

c) When is the glue at its hardest?

 

I think you mean H=2000+(h-7)^2 (lowercase h)

a) dH/dh=3(h-7)^2

b) dH/dh (0)=3(0-7)^2=49*3=147

c) Set dH/dh=0. h=7

 

yup thanks!

 

I have a 99 in this class :3 if you need any more help just msg me ^^
Dervs ftw.