Question

use differentials to determine by approximately how many centimeters does the diagonal of a square table increase if its area is increased from 50 square centimeters to 54.45 square centimeters?

Area= s^2
Diagonal= sqrt(2s^2)
so, D= sqrt(2A)

dD=A^(-1/2) dA
dD= 50^(-1/2)* 4.45
dD=0.62932...

BUT IT SAYS THIS ISNT THE CORRECT ANSWER

Answer 1

if the diagonal is d and the area is a, then we have

d^2 = 2s^2
a = s^2 = d^2/2
now forget all that square root stuff, and use implicit differentiation:

da = d dd
we have
a = 50, so d = 10
da = 4.45

4.45 = 10 dd
dd = 0.45

You made a mistake in the line
dD=A^(-1/2) dA
It should be
dD=(2A)^(-1/2) dA