Question

If f(x) = ∫et2(t – 2)(t – 3) for t ∈ [0, x] for all x > 0 then

(a) f has a local maximum at x = 2

(b) f is decreasing on (2, 3)

(c) there exist some c ∈ (0, ∞) such that f"

(c) = 0 (d) f has a local minimum at x = 3.

Answer 1

Correct option (a, b, c, d)

Explanation:

Clearly, has maximum at x = 2 and minimum at

x = 3 and f(x) decreasing in (2, 3)

So, by Rolle’* Theorem f'(x) = 0 for x = 2 and x = 3.

Thus, there exists a point c ∈ (2, 3) such that f"(c) = 0.