Arectangle initially has dimensions 3 cm by 6 cm. all sides begin increasing in length at a rate of 3 cm divided by s 3 cm/s. at what rate is the area of the rectangle increasing after 21 s?

  405 cm²/s

Step-by-step explanation:

The dimensions are increasing at the rate of 3 cm/s, so the dimensions in cm can be described as a function of time by ...

  3 + 3t

and

  6 + 3t

Then the area is the product of these, or ...

  A = (3 +3t)(6 +3t)

  A = 9t² +27t +18

and the rate of change of area is given by its derivative with respect to t:

  A' = 18t +27

When t=21, the value of this is ...

  A'(21) = 18·21 +27 = 405 . . . . cm²/s

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