Answer :

In the problems of rates in the application of derivates always look at the units of rates given, in this question the rates have units of distance/time.

= - 5 cm/minute, = + 4 cm/minute, (at x = 8, y = 6) = ?

There are two sides of rectangle x and y, so the area of the rectangle will be A = xy, and we have to calculate the rate of change of area with time.

A = x y

Differentiating both sides,

= 6( - 5) + 8(4) = - 30 + 32 = 2 cm^{2}/minute.

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