Question

A machine is set up to cut metal strips of varying lengths and widths based on the time (t) in minutes. The change in length is given by the function l(t) = t^2 - sqrt(t), and the change in width is given by w(t) = t^2 - 2t^(1/2). Which function gives the change in area of the metal strips?

Answer 1

Area(t) = Length * width
= L(t)*W(t)
=(t^2-sqrt(t))*(t^2-2t^(1/2))  
..... Please check, w(t) does not seem to have been posted correctly
=t^4-3t^2*sqrt(t)+2t
Differentiate with respect to t:
Area'(t)
=4t^3-(15/2)t^(3/2)+2