Solution
The correct answer is 6.05
Explanation
Let f(x)=√x where x=36
Let Δx=0.6
∴ f(x+Δx)=√x+Δx = √36+0.6
Now by definition, approximately we can write,
f′(x)=f(x+Δx)−f(x)Δx ----(i)
As f(x)=√x, f′(x)=12√x =12√36 =112
Putting these values in (i), we get
112 = √36.6−60.6
⇒ √36.6 = 0.612+6 = 6.05