Question

Each side of a square is increasing at a rate of 4 cm/s. at what rate is the area of the square increasing when the area of the square is 16 cm2?

Answer 1

The rate at which the area of the square is increasing when the area is 16 cm² is 32 cm²/s.

Step-by-step explanation:

To find the rate at which the area of the square is increasing, we need to differentiate the area function with respect to time. Let's denote the side length of the square as x and the area as A.

We know that A = x2 (since the square is a special case of a rectangle).

Now, let's differentiate both sides of the equation with respect to time t using the chain rule:

dA/dt = d(x2)/dt = 2x(dx/dt)

We're given that dx/dt = 4 cm/s. Substituting this value into our equation, we get:

dA/dt = 2x(4) = 8x cm2/s

Now, we can substitute the given area A = 16 cm2 into our equation to find the rate at which the area is increasing:

dA/dt = 8x = 8(4) = 32 cm2/s

Therefore, the rate at which the area of the square is increasing when the area is 16 cm2 is 32 cm2/s.

Answer 2

Confusing question but I would get 0, as if you have 4cm, that squared = 16cm^2. Therefore if it were increasing anymore, then you would not be able to get a value of 16.