Question

. At a certain instant, the length of a rectangle is 3 inches and is increasing at the rate of 1 inch per minute. At the same instant, the width is 2 inches and is decreasing at the rate of .5 inches per minute. Is the area increasing or decreasing

Answer 1

Answer:

Area is increasing

Step-by-step explanation:

Let x be the length of rectangle and y be the width of rectangle

We are given that

x=3 in

dx/dt=1 in/min

y=2 in

dy/dt=-0.5/min

We know that

Area of rectangle,$A=xy$

Differentiate w.r.t t

$\frac{dA}{dt}=y\frac{dx}{dt}+x\frac{dy}{dt}$

Substitute the values

$\frac{dA}{dt}=2(1)+3(-0.5)=2-1.5=0.5 in^2/min$

Hence, the area  of rectangle is increasing.