Suppose that 2 Joules of work is needed to stretch a spring from its natural length of 35 cm to a length of 54 cm. How much work is needed to stretch it from 50 cm to 55 cm?

First change cm to m.

W = the integral from Xi to Xf of kx dx

so W=(1/2)k(Xf^2) - (1/2)k(Xi^2)

So solve for k

2=(1/2)(k(.54^2) - k(.35^2))

4=k(.1691)

k=23.6546

them solve for W with your new k value but with a different distance

W=(23.6546/2)(.55^2 - .50^2)

W=.620975 J

But the answer is wrong....