if a square is increasing at a rate of 4cm/s from ALL sides, what is the rate the AREA is increasing at 25cm^2

Answer 1

A = x², so at A = 25, x = 5.

By the chain rule:

A' = 2xx' = 2(5)(4) = 40cm²/s

I think. been a long time.

Answer 2

Area, A = Length, L²
when A = 25cm², L = 5cm
dA/dL = 2L
Rate of change of sides, dL/dt = 4cm/s

So, when L = 5cm,
dA/dt (rate of change of area)
= dA/dL x dL/dt
= 2 x 5 x 4
= 40cm²/s

Hope this helps=)