Finding the Rate of Change of Area with Decreasing Length and Increasing Width

[kioria]

Hi,

I was practising differentiation and came across a some what rather easy question which I could not do. Can anyone direct me as usual. (this place is becoming my e-home). Mind you I am enjoying using LaTex converters haha.

Q. The length L of a rectangle is decreasing at the rate of 3 cm/sec, and the width W is increasing at the rate of 2 cm/sec. Find the rate of change of the area when L = 15 cm and W = 8 cm.

Thanks.

 

[Muzza]

dL/dt = -3 and dW/dt = +2. The area A is equal to W * L. Differentiate wrt t and plug in the values you were given.

 

[Chen]

W(t) = W₀ + 2t
L(t) = L₀ - 3t

A(t) = W(t)L(t)
A'(t) = W(t)L'(t) + W'(t)L(t)
A'(t) = -3(W₀ + 2t) + 2(L₀ - 3t)