Question

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

(A) f and f′ are continuous for x + 1 > 0

(B) f is continuous but f′ is not continuous for x + 1 > 0

(C) f and f′ are derivable at x = 0

(D) f is continuous at x = 0 but f′ is not

Answer 1

Answer is (A) f and f′ are continuous for x + 1 > 0

Here,

Both f and f′ are continuous for x + 1 > 0.