Question

Let f : R→R be given by f(x) = (x – 1)(x – 2) (x – 5).

Define F(x) = ∫f(t)dt, [x ∈ 0, x], x > 0.

Then which of the following options is/are correct?

(A) F has a local maximum at x = 2

(B) F has a local minimum at x = 1

(C) F(x) ≠ 0 for all x ∈ (0, 5)

(D) F has two local maxima and one local minimum in (0, ∞)

Answer 1

Correct option: (A, B, C)

Explanation:

F(x) has maxima at x = 2 and minima at x = 1 and x = 5

If maximum value of f(x) is negative then f(x) ≠ 0 for any x ∈ (0, 5)