Question

i have AP calculus problems i need help withAt a certain instance, 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

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?

Step-by-step explanation

as we know , area = length * breadth

so ,

`A=l* b`

differentiate with respect to t.

so ,

`(dA)/(dt)=l(db)/(dt)+b(dl)/(dt)`

now substitute the values,

`\begin{gathered} (dA)/(dt)=3(-0.5)+2(1) \\ \\ (dA)/(dt)=-1.5+2 \\ \\ (dA)/(dt)=0.5\text{ }inch\text{ }per\text{ }minute \end{gathered}`

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.