Given
Length = 3 inches , dl/dt = 1 inch/minute
width = 2 inches , db/dt = -0.5 inch/minute
Find
Is the area increasing or decreasing?
Explanation
as we know , area = length * breadth
so ,
[tex]A=l\times b[/tex]differentiate with respect to t.
so ,
[tex]\frac{dA}{dt}=l\frac{db}{dt}+b\frac{dl}{dt}[/tex]now substitute the values,
[tex]\begin{gathered} \frac{dA}{dt}=3(-0.5)+2(1) \\ \\ \frac{dA}{dt}=-1.5+2 \\ \\ \frac{dA}{dt}=0.5\text{ }inch\text{ }per\text{ }minute \end{gathered}[/tex]therefore , area is increasing at the rate of 0.5 inch per minute
Final Answer
Hence , the area is increasing at the rate of 0.5 inch per minute.
