Question

Using Rolle’s theorem, find the points on the curve Y=x2,x∈[−2,2] where the tangent is parallel to the x-axis.

Answer 1

Answer: Answer is (0,0)

Step-by-step explanation:

y = f(x) =x^2.......... (1)

1) This is an algebraic func. and is defined in [-2,2]. Therefore,

f(x) is cont. in [-2,2]

2) now, f'(x) = 2x

Here, f'(x) is defined in (-2,2)

So, f(x) is diffn. in (-2,2)

3) f(-2) =4 and

f(2)=4

So, f(-2)=f(2)

Hence, Rolle's theorem is applicable and there exists a point C belongs to (-2,2) s.t.

f'(C) =0

2C =0

C=0 i.e. x-coordinate

And y-coordinate =0........ {from (1)}

So, req point is (0,0)