Someone help me with this please... The length of a rectangle is given by 2t^2 + 3t – 7 and the height is sq. root of 2t, where t is time in seconds and the dimensions are in feet. Find the rate of change of the area with respect to time? Thank you!

1 Answer
Teddy
Jun 19, 2018

#(dA)/dt=5sqrt(2)t^1.5+4.5sqrt(2)t^0.5-3.5sqrt(2)t^-0.5#

Explanation:

The area of a rectangle is defined as the product of its length and height. Letting #A# represent the area of the rectangle as a function of time #t#, we get #A(t)=sqrt(2t)(2t^2+3t-7)#.
#A(t)=2sqrt(2)t^2.5+3sqrt(2)t^1.5-7sqrt(2)t^0.5#.
To find the rate of change of the area with respect to time, we differentiate both sides with respect to #t# and get
#(dA)/dt==5sqrt(2)t^1.5+4.5sqrt(2)t^0.5-3.5sqrt(2)t^-0.5#.

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