Answer
(a) $\frac{dx}{dt}=2\sqrt{2}$ units/s
(b) $\frac{dx}{dt}=4$ units/s
(c) $\frac{dx}{dt}=8$ units/s
Work Step by Step
Step-1: Differentiate $y=\sqrt{x}$ with respect to $t$, we get,
$$\frac{dy}{dt}=\frac{1}{2\sqrt{x}}\frac{dx}{dt}$$
$$\implies \frac{dx}{dt} = 2\sqrt{x}\frac{dy}{dt}$$
Step-2: It is given that $\frac{dy}{dt}=2$units/s. Thus, when $x=1/2$,
$$\frac{dx}{dt}=2\sqrt{0.5}\times 2=2\sqrt{2} units/s$$
Step-3: When $x=1$,
$$\frac{dx}{dt}=2\sqrt{1} \times 2 = 4units/s$$
Step-4: When $x=4$,
$$\frac{dx}{dt}=2\sqrt{4} \times 2 = 8units/s$$
