For $x \in[-2,2]$, let $f(x)=x^2+2$.

A. f(x) is continuous in [-2, 2]
B. f(x) is differentiable in (-2, 2)
C. f(-2) = f(2) = 6
D. f'(1) = 0

Choose the correct answer from the options given below:

A, B and C only

The correct answer is Option (4) → A, B and C only

$f(x)=x^2+2,x∈[-2,2]$

and,

polynomial function is always continuous and differentiable over it's entire domain.

now,

$f(2)=2^2+2=f(-2)=(-2)^2+2$

but,

$f(1)=(1)^2+2=3≠0$