Question

Let f(x) = ∫|t + 1|dt for t ∈ [-2, x]. Then 

(A) f(x) is continuous in [-1, 1]. 

(B) f(x) is differentiable in [-1, 1]. 

(C) f′(x) is continuous in [-1, 1]. 

(D) f′(x) is differentiable in [-1, 1].

Answer 1

Answer is (A), (B), (C), (D)

f(x) is a quadratic polynomial.

Therefore, f(x) is continuous as well as differentiable in [-1, 1].

Also f ′(x) is continuous as well as differentiable in [-1, 1].