Question

The greatest value of the function F(x) = ∫|t|dt for t∈[1, x] on the interval [-1/2, 1/2]  is given by

(A) 3/8

(B) - 1/2

(C) - 3/8

(D) 2/5

Answer 1

Answer is (C) - 3/8

F'(x) = |x| > 0 ∀ x ∈ [-1/2, 1/2]

Hence, the function is increasing on [-1/2, 1/2]. so,