Answer:
a) d(x)=
b)d'(x)=
c)The critical point is x=
d)Closest point is (,
Step-by-step explanation:
We are given the line
Let a point Q() lie on the line.
Point P is given as P(2,0)
By distance formula, we have the distance D between any two points
A() and B() as
D=
Thus,
d(x)=
But we have,
So,
d(x)=
Expanding,
d(x)= - - - (a)
Now,
d'(x)=
i.e.
d'(x)= - - - (b)
Now, the critical point is where d'(x)=0
⇒ =0
⇒ - - - (c)
Now,
The closest point on the given line to point P is the one for which d(x) is minimum i.e. d'(x)=0
⇒
as
⇒y=
So, closest point is () - - -(d)