Asked by Lorine
The length of a rectangle is given by 2t + 2 and its height is √t, where t is time in seconds and the dimensions are in centimeters. Find the rate of change of the area with respect to time.
A'(t)=
A'(t)=
Answers
Answered by
Damon
A = 2 (t+1)(t^.5)
dA/dt = 2 [ (t+1)(.5 t^-.5) + t^.5 (1) ]
= 2 [ .5 t^.5 +.5 t^-.5 + t^.5 ]
= 2 [ 1.5 t^.5 + .5 t^-.5 ]
= 3 sqrt t + 1/sqrt t
= (3 t + 1 )/sqrt t
dA/dt = 2 [ (t+1)(.5 t^-.5) + t^.5 (1) ]
= 2 [ .5 t^.5 +.5 t^-.5 + t^.5 ]
= 2 [ 1.5 t^.5 + .5 t^-.5 ]
= 3 sqrt t + 1/sqrt t
= (3 t + 1 )/sqrt t
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