H(t)=√(3t+2)
H(2)=√8=2√2; H(2.01)=√8.03. 2.01-2=0.01.
Rate of change=(√8.03-√8)/0.01=0.005298338/0.01=0.5298 approx.
An approximation is:
√8.03=√(8(1+0.03/8))=(√8)(1+0.03/8)½=(√8)(1+0.03/16)=(√8)(1.001875).
So √8.03-√8=0.001875√8, and (√8.03-√8)/0.01=0.1875√8=0.5303.